In the ending scene of the final episode of Angel Beats, Otonashi is seen but reincarnated. This does specify that he did pass on. Otonashi was the final person to pass on and stayed for a little while before finally disappearing. In Another Epilogue, it states that he was waiting for someone, but that 'someone' already passed. More information on this includes that he was able to 'meet back up' with the SSS, but in a heaven or reincarnated.
Another thing is that he didn't specifically fulfill his regrets, but disappeared anyway. Some people can make up ideas for what really happened. We all know, based on the ending scene in episode 13, that he did pass on, but for reasons we don't fully understand.
The main reason why he may have disappeared is that he finally realized that he did all he could, and he did save Angel's life, gaining a 'thank you' from her at the end when she passes. He may have stayed behind long enough to realize he needed to leave.
Another way we know he passed on is that in the ending scenes when everyone is disappearing from the picture, in the end, we can see Otonashi disappearing too. Signalling he did pass on to either become reincarnated with everyone else or to go to heaven. The final ending isn't as sad as we all think for Angel beats, considering everyone passes to the afterlife, potentially meets up again, and they all live happy lives.