The Englishman, 32, joins on a two-and-a-half-year deal and is Wolves’ fourth January signing.
Former West Brom centre-back Dawson, who has made 246 Premier League appearances, spent the past two seasons at the Hammers.
Wolves, who are 17th in the Premier League, face a trip to Manchester City (14:00 GMT) on Sunday.
Under new manager Julen Lopetegui the club have signed midfielder Mario Lemina, winger Pablo Sarabia and forward Matheus Cunha.
Dawson, whose last appearance for the Hammers was in an FA Cup win at Brentford on 7 January, was not registered in time to face City.
He initially joined West Ham on loan from Watford in October 2020 before turning that into a permanent move.
He made 87 appearances and scored five goals in all competitions for the Hammers, and started all six Europa League knockout round games last season as West Ham reached the semi-finals.
He impressed against a Sevilla side managed by Lopetegui when West Ham beat them in the last-16 of the competition.
Meanwhile, Wolves forward Fabio Silva is set to join PSV Eindhoven on loan for the rest of the season.
The 20-year-old spent the first half of the campaign in Belgium with Anderlecht, scoring seven goals in 20 league appearances, but will now switch to the Eredivisie, where PSV are two points behind leaders Feyenoord.
Uefa regulations mean Silva will be available for PSV’s Europa League play-off round game against Sevilla next month, even though he played for Anderlecht in the Europa Conference League.