Costa completed his medical on Thursday last week as cover for new signing Sasa Kalajdzic, who suffered a cruciate injury on his debut.

"It [my signing] wasn't in the best terms possible on accounts of a player's injury," Costa said.

The former Spain international added: "I can only wish him nothing but the best for him.

"But when he [manager, Bruno Lage] told me about returning to the Premier League since this a championship I have related to quite a bit, always liked it and followed.

"No matter how much I enjoyed playing in Madrid, I felt discouraged, but this motivated me. It lit that fire within me."

Costa, who is closing in on 500 career appearances, won the Premier League twice with Chelsea and claimed several trophies with Atletico Madrid in two spells for the Spanish club.

He had a trial with Wolves last week to assess his fitness and suitability.

Wolves are currently 14th in the Premier League table after only registering one win in six games this season.

"Diego will bring something unique to our dressing room and on the pitch," said Wolves chairman Jeff Shi.