The Reds have paid £23m for the Newcastle United midfielder with additional bonuses that could take the total to £25m.
The Dutch international will join up with the rest of the squad in America this weekend.
"Liverpool is a big club with a great history and it’s always a dream to play for as big a club as Liverpool," he told the official site.
When asked about Liverpool's chances of success this season, he added: "Everything is possible. You look at Leicester last season, they were champions. They put the marker down for a lot of teams and we have to try that also.
"Liverpool is a club with a great history but you want to get more history, create history, and be part of that. That’s what I want, I came here to win something, and I’m going to do everything to make it happen."
Wijnaldum will wear the number 5 shirt that has been vacant since the departure of Daniel Agger.