Streak is one of the most senior players to return to boost the southern African nation's flagging fortunes, following his dismissal as skipper in April last year when he objected to certain members of the country's national selection panel.
"Former Zimbabwe cricket captain Heath Streak has signed a contract to play again for Zimbabwe," ZCU announced in a statement on Friday.
He last played for Zimbabwe during the February-March tour of the country by Bangladesh last year.
"I just need to finalise some aspects of my contract with Warwickshire County so that it ties in with my international commitments," Streak said in the statement.
"Otherwise I am ready to play for Zimbabwe when selected. I am putting my weight fully behind the captain, Tatenda Taibu, and the rest of the lads."
Once one of the world's top 10 bowlers, Streak, an all-rounder, joins the left-handed batsman Andy Blignaut, another senior member who signed a contract on Monday.
Blignaut is one of 15 mainly senior players who were sacked after they demanded Streak's reinstatement.
Two other returnees Gavin Ewing and Barney Rodgers have been turning out for the Zimbabwe team that toured Bangladesh last month and which is currently touring South Africa.
Zimbabwe's convenor of cricket selectors Masood Ebrahim said Streak will be eligible to turn out for Zimbabwe's national cricket team subject to form and fitness.