Rangers boss Stuart McCall says he feels sorry for Gael Bigirimana, but admits he should never have been signed.
Chris Gunter will stay at Reading, after the club took up the option to extend his deal by another year.
The 29-year-old has signed for the Hammers on an initial six-month loan deal but the club have an option to extend that to a three-year contract.
Wellington has been linked with a move to Upton Park for a number of weeks and becomes Sam Allardyce's fourth signing of the January transfer window following the acquisitions of Joe Cole, Sean Maguire and Marouane Chamakh.
Wellington, who can play as a main striker or operate on either wing, will now be competing with Chamakh, Andy Carroll and Carlton Cole 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.
Allardyce will be hoping Wellington could be the answer to the lack of firepower, with the Brazilian having finished last season as Cruzeiro's top scorer with an impressive 27 goals.
Wellington said he has moved to West Ham to showcase his talents outside his home country and is not worried by the pressure of playing in the Barclays Premier League.
"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."