When did Old Slavic ЪI become Ы?
The question would be better asked as “When did the OCS ЪИ become ЪІ and when did ЪІ become Ы?” The three variants were originally used interchangeably, but later Ы took over, the most obvious reasons being it had the simplest shape of the three and since the yers disappeared as sounds it became irrelevant which one to use, ЪІ or Ы.
The first dated Cyrillic printed book Octoechos, 1491, in Kraków, by Schweipolt Fiol, had the letter as Ы, and since then all the printed Cyrillic books followed that trend. You can see lots of Ыs in this spread from the Octoechos, the first one is about the middle of the top line of the left page:
So the answer to your question is: by the end of the 15th century AD Ы became the only one.