Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
Blackpool have signed Rochdale full-back Tom Kennedy on loan, while Tangerines striker Francois Zoko has joined Bradford.
The 36-year-old will join up with his new City teammates on Wednesday and will be at the Etihad Stadium until January.
It is a short-term move for Lampard who signed in July for New York City, the MLS club owned by Manchester City and baseball giants New York Yankees.
On Friday it was reported the club was in talks with Lampard's representatives and immediately after City's shoot-out defeat by Olympiakos in the US on Saturday, manager Manuel Pellegrini confirmed the move had been completed.
Pellegrini said: "From Wednesday, he will start working with us and play for us until January."
When asked if Lampard was acquired just to improve his fitness for the MLS campaign which begins in March, the Chilean added: "He’s a member of the squad and he will fight for his position.
"He knows we have a good team and we have a lot of games in the Champions League so he's very important for our team."
It had initially been thought the player had agreed an autumn switch to join City's sister side Melbourne City where he would play alongside New York City teammate David Villa to improve his fitness and so this news will be a disappointment to Australian football fans.
It was also confirmed that Lampard would be available for the Premier League showdown with his old club Chelsea on Sunday, September 21.
On this fixture, Pellegrini added: "I will talk about that with him but he is a player for Manchester City and he will play every game that he needs to play."
This may raise some eyebrows at Stamford Bridge, with the England midfielder suggesting last year he would not play for another top-flight club in England.
He said in May 2013: "I can't imagine playing for anyone else after being 12 years at Chelsea. I've got a lot of respect for a lot of other Premier League clubs, particularly the top ones, but I'm not sure I could have done that."
Lampard scored 211 goals in 649 matches for Chelsea, becoming the club's record goalscorer and winning 11 major trophies in the process but was released by the club at the end of the season.
Lampard, who signed a two-year deal with New York City on July 24, is still considering his England future.
Sky Sports News football reporter Kaveh Solhekol was at Pellegrini's news conference at the TCF Bank Stadium in Minneapolis on Saturday, and said that even a player of Lampard's stature would have his work cut out to earn a starting place amid stiff competition.
"According to Pellegrini, this is not a PR stunt," said Solhekol.
"Lampard is not moving to Manchester to sell shirts or to stay fit. He is moving to Manchester to fight for his place and to play at the highest levels of European football for at least another five months.
"The fight to get into the City starting XI is going to be quite a challenge, even for a player who has won every major club trophy in the European game.
"City have arguably the strongest midfield in English football. Next season, Pellegrini will be able to choose from Yaya Toure, Fernando, Fernandinho, Lampard, David Silva, Samir Nasri, James Milner, Jesus Navas, Javi Garcia, Jack Rodwell and Scott Sinclair.
"Keeping all those players happy - if they all stay at City - will be a difficult, but Pellegrini is convinced that City need strength in depth to compete on four fronts next season."
Pellegrini went on to confirm that Lampard would stay at City until January and he hinted that he was now going to concentrate on one more transfer deal.
That deal will almost certainly see France defender Eliaquim Mangala moving from Porto for about £30m.
“Our transfer business doesn’t need to be completed today,” Pellegrini said. “We have time to analyse the squad and see what needs to be done.”