Woodman joined Liverpool on a free transfer from Preston North End last summer and made four appearances during his debut campaign, including three in the Premier League. He is now set to remain part of Andoni Iraola's senior goalkeeping group after putting pen to paper on fresh terms.
"I'm absolutely delighted, to be honest," Woodman told Liverpool's official website. "Off the back of last season, personally it was amazing for me and then to come back in pre-season and there be an offer for me from the club to stay here longer, I was made up. I'm just so happy that I could re-sign here and be a part of this amazing club.
"[I feel] pride and so many emotions, really. Last season I came in and did the role I was doing and then when I got the opportunity to play, especially the Palace game, it just felt like a real connection to the fans and just a massive understanding of them. Now I get the chance to stay here for longer and to be a part of it again is unbelievable, and me and my family are delighted."
Elsewhere in Liverpool's goalkeeping ranks, midfielder Tommy Pilling is expected to complete a permanent move to Slovakian side MFK Zemplin Michalovce, bringing an end to a 16-year association with the club that began when he joined the academy aged five.
The St Helens-born midfielder made the bench for two Carabao Cup ties last season but is yet to make his senior debut, and the move represents a chance to establish himself in first-team football elsewhere.
Meanwhile, 19-year-old academy goalkeeper Kornel Misciur is close to agreeing a loan move away from Anfield, with a number of non-league clubs having registered an interest.
Misciur was included in Liverpool's Champions League squad last season and sat on the bench six times in the competition, including both legs of the quarter-final against Paris Saint-Germain, but has yet to make his senior debut for the club.