The mid-table Premier League side said in a statement that the 29-year-old holds a European Union passport and therefore does not require a work permit.
"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," the former Botafogo forward said.
"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 a first or second striker."
Wellington, who has netted 39 goals in 110 Brazilian Serie A and Copa Libertadores matches for Cruzeiro but has never played for his country, joins Marouane Chamakh and Joe Cole as attacking recruits at West Ham during the January transfer window.
Morocco striker Chamakh joined on loan after falling down the pecking order at Arsenal under Arsene Wenger while Cole returned to his boyhood club after a difficult spell at Liverpool.
England forward Andy Carroll is still on a season-long loan from Liverpool while West Ham boss Sam Allardyce also boasts Carlton Cole, Ricardo Vaz Te and Modibo Maiga as striking options. (Writing by Mark Meadows; editing by Tony Jimenez)