The 28-year-old has sealed a deal to return to the La Liga side in January, having being frozen out by Conte following a season which saw the Spain international score 20 times to help them win the Premier League title.
Conte and Costa reportedly had a very strained relationship in the build-up to his exit, and the Italian was cagey when asked to comment on Costa at his weekly press conference this afternoon.
"We want to thank him for what he did with this club. We wish him the best for the future," he told reporters.
"Now [our relationship] is not important. I'm not interested to continuing talking about this issue. I'm working with players, I'm very happy to work with these players, now it's not important.
"The past is not important. For every coach, every single player, the past stays there. If you did well in the past it's okay but we have to work for the present and above all for the future.
"I don't forget that we won together last season. I repeat for sure we want to thank him for his effort last season, not only last season but the period he played for Chelsea."
During his three seasons at Stamford Bridge, Costa won two Premier League titles and the League Cup.