The 28-year-old missed last weekend's win at Leicester with a back injury amid reports of a bust-up with Conte and his backroom staff.
Costa has also been linked with a move to the Chinese Super League.
Conte said on Friday: "Yes
He's available for the game against Hull City
He restarted having training sessions on Tuesday with the rest of the team.
"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."
Chelsea have a seven-point lead entering this weekend's fixtures and play at home to Hull on Sunday.
Conte was asked if Chelsea should tie Costa down to an extended contract to end speculation over his future.
"I think now it's better to be focused, to be concentrated on the present, not on the future," he added.
"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."
Conte refused to directly address questions over the reported training ground argument and would not confirm if he met with Costa individually this week.
And the Italian insisted Costa trained on his own on Sunday and Monday, while his team-mates had time off, to be in the right physical condition to rejoin first-team training on Tuesday.
Conte said: "After the game against Leicester I told you the truth and I repeat: I heard a lot of speculation about Diego.
"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 did confirm Chelsea are considering an offer from Bournemouth for second-choice goalkeeper Asmir Begovic, back-up to Thibaut Courtois.
Conte said: "Asmir is an important player for me, on and off the pitch
He knows this.
"There is this offer
The club and I are evaluating this offer."
Source : PA