The make-up of the Rebel Council is described in the Rogue One Visual Guide as a combination of military leaders and sympathetic senators:
The upper command staff of the Alliance military are known as the rebel council in common parlance and also include a civilian component of senators.
A number of council members at the time of Rogue One are identified in the book:
General Airen Cracken, who seems to be head of Alliance Intelligence; his role is filled in the film by Davits Draven, head of Yavin 4 Intelligence.
It falls to Davits Draven to represent Alliance Intelligence on the rebel council and at the Yavin base, as General Airen Cracken is busy setting up spy networks in the Outer Rim.
General Pitt Onoran, head of Yavin 4 Special Forces
Onoran heads up the Yavin 4 Special Forces division. He earned valuable experience as a logistics officer in the Republic army during the Clone Wars.
Since Onoran is specifically called out as only being in charge of Yavin 4 SpecForces, it seems likely that he has a superior officer (as Cracken is superior to Draven), but they are not named or identified
Colonel Haxen Delto, an intelligence operative in charge of signals intelligence
Delto oversees the specialists who scour HoloNet and subspace transmissions for patterns and packets of usable intelligence. His methodical approach stands all in good stead.
Considering his position, Delto is likely subordinate to Draven and Cracken.
Major Capin Harinar, an intelligence analyst subordinate to Draven
Part of General Draven's Alliance Intelligence staff, materials analyst Harinar examines captured Imperial technology to assess the capabilities of the enemy and plan countermeasures.
General Antoc Merrick, head of Yavin 4 Starfighter Command
As part of the rebel council, Merrick has a voice in the direction of the Rebellion in these pivotal days.
Colonel Bandwin Cor, a senior officer in Alliance Starfighter Command, who apparently does most of the actual work
While General Merrick oversees Alliance Starfighter Command, he defers to Colonel Cor for day-to-day decisions.
Colonel Anj Zavor, liaison to Admiral Raddus
The Yavin 4 liaison to Admiral Raddus, Colonel Anj Zavor works as part of Fleet Command. Zavor keeps a channel of communication open between the base and the ever-mobile Admiral.
Presumably Raddus himself also holds a seat on the council, if he ever sat still long enough to attend meetings, and indeed the novelization has him attending Jyn's debriefing:
Admiral Raddus — a Mon Calamari with skin mottled like storm clouds and unblinking amber eyes — sternly asked her about her initial parting from Saw Gerrera; she made up a lie about her discomfort with Saw's methods that seemed to satisfy him.
Rogue One: A Star Wars Story - Official Novelization Chapter 14
General Baccam Grafis, head of procurement
Grafis heads up Ordnance and Supply - the procurement of essential materiel for the Rebellion. He pursues lines of supply for starship-grade fuel and weaponry.
General Dustil Forell, head of transportation
Forell oversees Support Services, a division dedicated to the Alliance's anemic transportation network.
General Jan Dodonna, sector commander for the Yavin group
As the Sector Command officer for the Yavin-based rebels, General Dodonna is an important voice on the rebel council.
The young reader's novel Moving Target, set after Empire Strikes Back, identifies several more possible candidates, who may or may not have been part of High Command at the time of Rogue One:
The Alliance's top leaders were standing together in an arc. General Cracken, the intelligence chief, was standing next to the careworn General Carlist Rieekan, who'd been in charge of the rebel defenses on Hoth — and whose immediate evacuation order had saved many lives. Next to Rieekan stood General Madine, a cocksure Corellian from the Alliance's special-operations wing. Beside them stood Admiral Ackbar, the salmon-colored, goggle-eyed Mon
Calamari strategist who commanded the fleet.
On one side of the space stood a number of top admirals and generals—she recognized the grim, hatchet-faced Admiral Nantz and the green-skinned Duros Admiral Vassa, along with General Veertag and General Tantor.
A Mon Calamari admiral Leia didn't know raised her hand.
Moving Target: A Princess Leia Adventure Chapter 4: "Resurrection of Evil"
Since the Alliance (the military branch, at least) is structured like an ideological militia, it's likely that the military members of the council are promoted into the position according to their aptitudes.
In addition to the military branch, the rebel council also has a group of civilian leaders, most of whom are senators (and ex-senators):
Mon Mothma, the Alliance head of state
Arranged beneath Mon Mothma, the titular chief of state of the Alliance Civil Government, is the Cabinet - a collection of six allied ministers with specific areas of responsibility.
Senator Nower Jebel
Senator Nower Jebel of Uyter is the Minister of Finance in the Alliance Cabinet. Jebel believes a negotiated peace settlement is possible, and the time for violence may be at an end.
Senator Vasp Vaspar
Vasp Vaspar serves as senator of the Taldot sector and as the Alliance's Minister of Industry, overseeing the fledgling Rebellion's meager yet vital resources.
Bail Organa. I'm not sure what Bail is minister of, but he got his position in the Alliance presumably because he helped fund it, and because his home planet of Alderaan provides the bulk of their resources.
Senator Tynnra Pamlo
Senator Tynnra Pamlo of Taris is stirred by whispers of the Death Star. As Minister of Education, the liaises closely with Alliance Intelligence and has been exposed to evidence of the Empire's worst atrocities.
The remaining two cabinet members are unidentified. It's also not clear how they're appointed; if the Alliance Civil Government behaves like democratic governments in our world, the various cabinet members are likely appointed to their position by Mon Mothma.