The International Tennis Federation (ITF) said players from the two countries could take part in the Paris Games as neutrals without flags, emblems or anthems.
Russians and Belarusians were banned from competing internationally following Russia's invasion of Ukraine in 2022, for which Belarus has been used as a staging ground.
In March last year, however, the IOC issued a set of recommendations for international sports federations to allow competitors from these countries to return.
Speaking before his Indian Wells opener on Friday, Russian Medvedev said he was looking forward to playing in the Olympics after a positive experience in Tokyo three years ago when he made the quarter-finals of the singles competition.
"If I can, I'm going to be there. I'm going to play singles and doubles," Medvedev told reporters.
"When I was in Tokyo it was an amazing experience. It was probably one of the biggest memories of my sporting life, which I was surprised (by) because in tennis, we tend to think that the Grand Slams are more important.
"About the neutral flag, I'll follow the rules. If it's under a neutral flag I'll play under a neutral flag and I'm going to try to compete there, show good tennis and try to win, for sure."
Russian and Belarusian players already compete on the ATP and WTA tours as neutrals.
The Olympic tennis event will begin on July 27.
