Amid dizzying activity in the closing hours of the close-season transfer window, Arsenal grabbed the headlines with a sensational swoop for Ozil worth a reported fee of £42.4 million ($66 million, 50 million euros).
The move came on the day that Gareth Bale was presented as a Madrid player after leaving Arsenal's arch rivals Tottenham Hotspur for a fee of around £80 million, paving the way for Ozil's exit.
Arsenal said Ozil had signed a "long-term contract," with a reported duration of five years, after he underwent a medical examination in Munich.
"We are extremely pleased to have signed Mesut Ozil," said long-serving Arsenal manager Arsene Wenger, who had come under pressure from the club's fans to deliver a major signing.
"We have watched and admired him for some time as he has all the attributes I look for in an Arsenal player."
Ozil told the Arsenal website: "I am thrilled to be joining a club of the stature of Arsenal and am looking forward to playing in the Premier League."
Arsenal, who had never previously spent more than £15 million on a player, also announced the signing of 27-year-old Italy international goalkeeper Emiliano Viviano from Palermo on a season-long loan.
Ozil's transfer was the most significant development on a day when gross spending by Premier League clubs during the close-season transfer window surpassed £500 million for the first time, according to financial consultants Deloitte.
After a frustrating first summer as United manager, David Moyes brought in Belgian midfielder Fellaini, with whom he worked at Everton, in a deal worth £27.5 million.
"Manchester United is delighted to announce the signing of Belgian midfielder Marouane Fellaini from Everton," said a statement on United's website.
Manager David Moyes added: "He is a player with great ability and strength and I think he will make a real difference to our squad."
Fellaini said he was "thrilled" with the move and that he "jumped at the chance" to renew his relationship with former Everton boss Moyes.
Everton earlier confirmed the sale, adding that the price tag was £27.5 million.
However, the reigning English champions missed out with approaches for Madrid's Portuguese left-back Fabio Coentrao and Athletic Bilbao midfielder Ander Herrera.
Britain's Press Association claimed United were too late in submitting their request to sign Coentrao on loan, while bizarre reports from Spain said the move for Herrera collapsed after three imposters claiming to represent the club found their way into the Spanish league offices.
Everton also sold striker Victor Anichebe to West Bromwich Albion for a fee that could rise to £6 million, but they signed Irish midfielder James McCarthy in a £13 million deal from Wigan Athletic.
Moyes's successor, Roberto Martinez, was also able to seal loan moves for Manchester City midfielder Gareth Barry and Belgian striker Romelu Lukaku, who was allowed to leave Chelsea despite impressing on loan at West Brom last season.
Current Premier League leaders Liverpool completed three transfers earlier in the day.
Defenders Mamadou Sakho and Tiago Ilori joined from Paris Saint-Germain and Sporting Lisbon respectively, while winger Victor Moses arrived on a season-long loan from Chelsea.
Liverpool reportedly paid a combined amount of £25 million to sign Ilori and France international centre-back Sakho, who had fallen down the pecking order at PSG.
"I came here because the project that is in place at Liverpool interests me," Sakho, 23, told Liverpool's official website.
Aston Villa made Czech international striker Libor Kozak their seventh new recruit of the close-season, signing him from Lazio on a four-year contract for a reported fee of around £7 million.
West Brom broke their transfer record to take Benin midfielder Stephane Sessegnon from Sunderland, who signed Italian striker Fabio Borini on loan from Liverpool and left-back Andrea Dossena from Napoli.
Seven months after his aborted exit from West Brom on the final day of the January transfer window, when he drove to Loftus Road in hope of joining Queens Park Rangers, Nigerian striker Peter Odemwingie left the Hawthorns to join Cardiff City on a two-year contract.