The 29-year-old, who has scored 10 goals for Cruzeiro this season, joins on an initial six-month loan deal but the club have an option to extend that to a three-year contract.
Paulista was also the club's top scorer last term with an impressive 27 goals, and is the latest arrival in a busy January for the Hammers.
Manager Sam Allardyce has been particularly active in bolstering his attacking options with old boy Joe Cole returning on a free transfer and Arsenal striker Marouane Chamakh signing on loan.
"I think I can do my best here and I am coming to England to prove to everyone that I am one of the best strikers in Brazil and to get better and better," he told West Ham TV.
"I am strong, I am a fighter and I can score with both feet. I run a lot on the pitch and I can play as either as first or second striker.
"The pressure will not be a problem for me because I am used to it from my time in Brazil, where the fans were really addicted to the club. The manager also put pressure on the players too, so it will be the same playing here."
West Ham co-chairman David Sullivan labelled the signing of Wellington as a 'wildcard' but is sure he will be a hit at Upton Park.
"I'd like to welcome Wellington Paulista to east London and West Ham United," Sullivan said.
"He is another exciting player to add to our squad and although he may not be that well known on these shores, he comes with an excellent track record in Brazil.
"His arrival is similar to some of the other 'wildcard' players we have signed before like in Demba Ba and Ilan.
"They both made significant contributions and if he can match their efforts he will be an excellent acquisition for West Ham United."