The 29-year-old joined the club on a free transfer last summer to strengthen their goalkeeping options and has now committed his future to Anfield with a contract extension.
“I’m absolutely delighted, to be honest,” Woodman told Liverpoolfc.com.
“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.”