Speaking to reporters on Wednesday, Prescott said he will "be ready when it matters" and thanked Alex Smith for his support throughout the recovery process.
"I have to thank Alex Smith," he said. "At that moment when you're sitting there and you have an injury like that...to see somebody who has already done it – and did it actually in worse circumstances, that allowed my mind to go 'I can do this.'"
Washington Football Team doctors cleared Smith for full football activity last August. He wound up going 5-1 in six starts to help the team win the NFC East for the first time since 2015.
ESPN's Todd Archer reported the recovery timetable for Prescott is 4-6 months.
Per NFL Network's Tom Pelissero and Ian Rapoport, Prescott underwent a second procedure on his ankle in December that wasn't directly related to the original surgery, but it was used "to strengthen his deltoid ligament, clean out the ankle and make it more structurally sound."
The Cowboys don't seem concerned about Prescott's ability to return to his Pro Bowl form going forward. They officially announced his signing on Wednesday. ESPN's Adam Schefter reported the deal includes $126 million guaranteed and up to $160 million total.
Schefter also noted Prescott's contract is actually a six-year deal, but the last two are voidable to help the Cowboys with the salary cap.
Prescott has gone 42-27 in 69 starts and has led the Cowboys to two NFC East titles over the past five seasons. The 27-year-old set career highs with 4,902 passing yards and 30 touchdowns in 2019.