Papa Bouba Diop, Richard Hughes and Niko Kranjcar are all out injured, while Lassana Diarra departed for Real Madrid earlier this month.
The signings continue a busy transfer window for Adams, who has already brought in Jermaine Pennant on loan from Liverpool, while Jermain Defoe left to rejoin Tottenham.
Mullins has spent the last five years at West Ham after joining from Crystal Palace and he has made 21 appearances for the Hammers this season.
"It was in a little bit of a shock," he told Portsmouth's website. "I trained on Sunday with West Ham and then it all happened very quickly, but I'm very pleased to have joined.
"It was a great experience to have worked under Gianfranco Zola but it's a great challenge here to come and work with some really talented players.
"I enjoyed my time at West Ham but I was there for five years and thought that maybe it was time for a change.
Adams happy with with new recruits
"Portsmouth are a club with a lot of history. They won the FA Cup last year, so I'm very excited to be here."
Portugal under-21 international Pele, whose full name is Vitor Hugo Gomes Passos, is an attacking midfielder and has previously played for Inter Milan.
"It's always been an ambition of mine to play in England, to play in the Premier League," he said. "I've always watched English football, and the crowds are always great here.
"England is the home of football, so it's fantastic to get this opportunity."
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