"I am honoured to be appointed as captain. The club has a proud history and I'm looking forward to working with the players, staff and supporters to bring more silverware in the future," Streak said.
"I've enjoyed playing for Zimbabwe immensely but I have decided to retire from international cricket in order to fulfill my contractual commitments with Warwickshire.
I hope that one day I can assist Zimbabwe cricket again in its efforts to develop," the Zimbabwe pacer was quoted as saying in the ICC website.
Warwickshire have confirmed that Streak has been appointed as their captain for the next two seasons.
Streak, who has spent the last two summers at Edgbaston, reportedly wanted to be away from the constant in-fighting in Zimbabwe cricket.
Although he has been offered a new contract by Zimbabwe Cricket Union he did not sign it and the offer from Warwickshire led to his decision to quit international cricket.
Streak joined Warwickshire in 2004, and although his appearances were limited by international calls, he made a strong impression and his appointment will be welcomed by both players and spectators alike.