The 28-year-old forward, who has also had spells at Alaves and Botafogo, has been linked with a move to Upton Park for some time and Press Association Sport understands the deal could be completed by Friday evening.
West Ham boss Sam Allardyce has been keen to strengthen his attacking options in the transfer window and has already moved to bring in Liverpool midfielder Joe Cole and signed Arsenal striker Marouane Chamakh on loan until the end of the season.
Wellington, who can also play on either wing, would be competing with Chamakh, as well as Carlton Cole and fellow loanee Andy Carroll for a berth in West Ham's attack.
The Hammers have struggled to find goals from their forwards for much of the season with midfielders Kevin Nolan and Mark Noble leading the scoring charts with nine goals between them.
Wellington could be the answer to the lack of firepower in Allardyce's front line, having finished last season as Cruzeiro's top goalscorer with an impressive 27 goals - with 10 to his name so far this campaign.