Disney Canon
No explanation has been given for either Jedi Master's absence (although Yaddle's Databank entry confirms that she was no longer on the council). It is unlikely that we will ever get an explanation, since Disney does not seem interested in exploring things that happened pre-Clone Wars.
Legends
Yarael Poof
His final appearance was in the comic mini-series Zam Wessel, set in 27 BBY (5 years after The Phantom Menace, 5 years before Attack of the Clones).
The story involved the Infant of Shaa, an artifact that could store Force energy. A terrorist group tried to unleash that energy on Coruscant so that an enormous disturbance in the Force would eradicate life on Coruscant. After forming an uneasy alliance with bounty hunters Jango Fett and Zam Wessel, Yarael Poof was fatally stabbed with a vibroblade and, with the last of his effort, disarmed the artifact and saved the planet.
Coleman Trebor was selected as his replacement on the Jedi council.
Yaddle
Yaddle's fate is detailed in the book Jedi Quest: Shadow Trap. In the year 25 BBY (7 years after The Phantom Menace, 3 years before Attack of the Clones), Yaddle went on a diplomatic mission with Obi-Wan and Anakin to the war-torn world of Mawan. She sacrificed her life to save millions of people from being killed by a bioweapon.
Yaddle hung above [Anakin], above the tallest building of Naatan, the Force holding her temporarily aloft. She held a silver canister against her chest. [...]
"No!" he shouted. But he could already feel it. Yaddle was drawing in the great net of the Force she had created, drawing it around her so tightly and fiercely and strongly that Anakin fell to his knees. He had never felt the Force move like this. He couldn't speak or move.
From far below, Granta detonated the explosives.
Anakin heard a sharp pop, nothing more. The Force grew until Anakin was dazzled. Instead of exploding, the canister imploded, and Yaddle drew the toxic gas and the explosive power in, absorbing it into her body.
Then she simply disappeared. A shower of light particles swirled, hung in the air, then evaporated.
Anakin's face was wet. Tears flowed and he did not feel them. The night sky was empty, and Jedi Master Yaddle was dead.
Yaddle was replaced by Shaak Ti on the Jedi Council.
Out of universe
It wasn't because they were puppets
One might think that because Yarael Poof and Yaddle were puppets in The Phantom Menace, they were replaced because using puppets would be impractical for the Battle of Geonosis in Attack of the Clones. Turning them into CGI, as they did with Yoda, would be costly, but that doesn't seem to have been an issue. Attack of the Clones animation director Rob Coleman talked about Yarael Poof's replacement, Coleman Trebor, and noted that he was a fully CGI character who was only on screen long enough to get killed by Jango Fett.
Coleman Trebor was named, the maquette was realized as a computer-generated character, the character was painstakingly animated and composited into the temple and arena scenes...
... and then Coleman Trebor was quickly iced by Jango Fett.
So they were definitely capable of keeping those two Jedi Masters, but chose not to.
George Lucas thought Yarael Poof would be confused with a Kaminoan
Rob Coleman recalls that George Lucas was concerned that Yarael Poof would be confused with the Kaminoans, the species that Obi-Wan discovered were creating the Clone Army.
"If you think back to the original Jedi Council there was a long-necked Jedi on the far side -- Yarael Poof -- he was a puppet. George was afraid that if we kept that guy in, people might confuse him with the Kaminoans."
It's not entirely clear why Yaddle was replaced
I have not been able to find any particular reason why Yaddle was killed off. However, I speculate that if the audience had already seen Yaddle jumping around in the Geonosian Arena, it would be less of a spectacle to see Yoda battle Count Dooku later in the film, and so she was removed for that reason.
