This is covered in the film's new Disney canon junior novelisation. In short, his reward (in the boxes we see on screen) is made up of **precious metals that are evidently used in the repair of spaceships.**

> *“We don’t keep that sort of money lying around,” Commander Willard
> said. “And this is…we need every cent to keep up our operations.” **“I’m
> willing to accept the amount in precious metals if you don’t have the
> credits on hand,”** Han said, crossing his arms over his chest. “Come
> on, pal, you don’t want word to get around that the Rebellion can’t
> honor their debts, do you? No one would be willing to do business with
> you.”*
> 
> ...
> 
> ***“Give him whatever he wants,”** Leia said stiffly. The look she shot Han
> could have incinerated half the Death Star. “The sooner he gets it,
> the sooner he’s gone.”*
>
> <Sub><sup>[A New Hope: The Princess, the Scoundrel, and the Farm Boy][1]</Sub></sup>


A similar scene occurs in the earlier [A New Hope: Junior Novelisation][2]. 

> *Stepping down to the hangar floor, Luke found Han and Chewbacca
> loading small boxes onto an armored military speeder. **The boxes
> contained precious metals, the only form of currency that Han would
> accept from the Alliance. Han had insisted on the payment, even though
> the Rebels desperately needed the materials for repairing starships
> and equipment.** Han appeared to be completely ignoring the activity of
> the Rebel flight crews and pilots.*
>
> <sub><sup>[A New Hope: Junior Novelisation][2]</sub></sup>

Moving down the canon scale, this is also backed up in the (alas, now non-canon) [Star Wars Radio Dramatization][3]:

> **Leia:** *Captain Solo may have no morals whatsoever, Commander, but he's right. Both Luke and I promised him payment for his and
> Chewbacca's help in this matter.*
> 
> **Willard:** *Very well, I see I misjudged you, Solo*
> 
> **Han:** *I'll cry later. Right now, I'll settle for cash. In small, used notes if you've got 'em.*
> 
> **Willard:** *But this is a Rebel camp! We're hunted people, with very little Imperial currency among us!*
> 
> **Han:** *Oh. Well, **your tech facilities must have stocks of precious metals.***
> 
> **Willard:** *Yes...*
> 
> **Han:** *They'll do.*
> 
> **Willard:** *But **those are critical matériel! We need those metals for repairs, to keep our weapons and equipment functioning!***
>
> <sub><sup>[Star Wars Radio Dramatization][3]</sub></sup>

  [1]: https://starwars.fandom.com/wiki/A_New_Hope:_The_Princess,_the_Scoundrel,_and_the_Farm_Boy
  [2]: https://starwars.fandom.com/wiki/Star_Wars_Episode_IV:_A_New_Hope_%28junior_novelization%29
  [3]: https://en.wikipedia.org/wiki/Star_Wars_%28radio%29