The 25-year-old midfielder, who had a medical with the Premier League side on Friday, has signed a five-year contract.
Wijnaldum joined Newcastle for £14.5m from Dutch side PSV in 2015, playing in all 38 of the club's Premier League games last season and scoring 11 goals.
He is the Reds' seventh signing of the summer so far.
The others are:
It is understood Liverpool will pay an initial £23m with a further £2m in conditional add-ons.
Wijnaldum will join the Reds on their pre-season tour of America, where they will play Chelsea (27 July), AC Milan (30 July) and Roma (1 August).
He began his career at Feyenoord before moving to PSV Eindhoven and has made 30 appearances for the Netherlands, helping them finish third at the 2014 World Cup.
He scored on his Premier League debut in August 2015 and found the net a further 10 times during the season, including four in a 6-2 win over Norwich, but could not prevent Newcastle being relegated to the Championship.
Liverpool finished eighth in the Premier League last season and a 3-1 loss to Sevilla in the Europa League final ensured they will not be playing in European competition in 2016-17.
Klopp's side begin their Premier League campaign away at last season's runners-up Arsenal on 14 August.
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Liverpool have signed Netherlands international Georginio Wijnaldum from Newcastle for £25m.