Both players will go straight into manager Tony Adams' squad for the side's Premier League clash with Aston Villa at Fratton Park.
Adams has had a busy month in the transfer market with Jermaine Pennant joining on loan from Liverpool last week and Nadir Belhadj signing a permanent contract. Jermain Defoe and Lassana Diarra have also left the club.
Mullins' move comes just two days after his final appearance for Gianfranco Zola's side as a substitute in the 2-0 FA Cup win over Hartlepool.
The 29-year-old, who has spent the past five years at Upton Park after an £800,000 move from Crystal Palace, only became aware of Portsmouth's interest late on.
Speaking to the Portsmouth website, Mullins said: "It was a little bit of a shock. I trained on Sunday with West Ham after the game on Saturday 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 to come here 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. Portsmouth are a club with a lot of history. They won the FA Cup last year, so I'm very excited to be here."
Pele, a Portugal Under-21 international, only joined Porto last summer after previously playing for Inter Milan and scoring in last year's Italian cup final.
Pele said: "It's always been an ambition of mine to play in England, to play in the Premier League. 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."
Portsmouth executive chairman Peter Storrie admitted both deals were concluded quickly.
Storrie said: "Tony and I decided to move for Hayden on Saturday night. We got hold of West Ham on Sunday morning and I think they were a bit surprised that we wanted to get the deal done so quickly.
"Hayden's an experienced player who has played exceptionally well against us in the past. He's a guy with immense experience in the Premier League, and that's what we need in this situation.
"He wanted regular football, because he has been in and out of the West Ham side.
"Pele's an exciting young talent. He did well for Inter before joining Porto. But there was a change of manager at Porto, who switched it around a bit, and the boy was desperate to move.
"I spoke to him on Saturday evening and he was on the plane here within 24 hours, which tells you exactly about his eagerness. He's an expensive player, so it's a deal with an option to buy so we can both have a look at each other."