A back problem was the official reason for Costa's absence at Leicester, but there were reports it stemmed from an angry row with fitness coach Julio Tous.
"He's available for the game against Hull City," Conte told a press conference at Chelsea's Cobham base southwest of London.
"He restarted having training sessions on Tuesday with the rest of the team."
Costa, Chelsea's top scorer with 14 league goals, was also reported to be the subject of a mega-money approach from Chinese club Tianjin Quanjian.
But Conte said: "I think the player wants to stay at Chelsea. He's very happy to play with us. This idea (to move) is far from his mind."
Conte would not be drawn when he was asked whether Chelsea should tie Costa down to a new contract in order to head off speculation about his future.
"I think now it's better to be focused, to be concentrated on the present, not on the future," said the Italian, whose side are seven points clear of Tottenham Hotspur at the top of the table.
"Diego is a good player. He's a good person. Now he's only focused on Chelsea and to play with us and to continue to help us.
"He missed only one game, the last game. Now he's ready to come back with us.
"I'm sure about his commitment, his behaviour, his will to fight with this team, to try together to fight to the end to try to win the title."
Costa refused to directly address the reports about Costa's alleged training-ground argument with Tous and would not say if he had held a meeting with the Brazil-born Spain striker this week.
Costa, who stands to make his 100th Chelsea appearance against Hull, trained on his own on Sunday and Monday, while his team-mates had time off, before returning to first-team training on Tuesday.
Conte said he had trained separately purely to help him build up fitness, rather than as a punitive measure.
"After the game against Leicester I told you the truth and I repeat: I heard a lot of speculation about Diego," said the Chelsea manager.
"But now the most important thing is he trained with us this week and the most important thing is he hasn't pain in his back.
"He's available to come back in our squad against Hull City."
Conte also confirmed Chelsea are studying an offer from Bournemouth for their second-choice goalkeeper Asmir Begovic.
"Asmir is an important player for me, on and off the pitch. He knows this," Conte said.
"There is this offer. The club and I are evaluating this offer."