The 40-year-old joins from Norwegian club Molde and succeeds Malky Mackay, who was sacked on December 27 after his relationship with club owner Vincent Tan broke down.
Wayne Rooney sat out United's 1-0 victory at Norwich City in the Premier League on Saturday, but played for the entirety of the 2-1 home defeat by Tottenham Hotspur on New Year's Day.
Goals from Fernandinho, Yaya Toure and Aleksandar Kolarov in a 3-2 win at Swansea City on Wednesday earned Pellegrini's side another valuable three points in their pursuit of the title.
It is nine years since Arsenal last won a trophy and 10 years since they won the league, but the last-gasp 2-0 New Year's Day win over Cardiff City confirmed their credentials as championship contenders.
The Manchester United manager was incensed by a late decision not to award United a penalty kick in a
Brazil midfielder Oscar had only been on the pitch for a matter of seconds in Chelsea's 3-0 win over Southampton when he went into the book for diving in a failed attempt to win a penalty.
Emmanuel Adebayor and Christian Eriksen scored fpr Spurs to all but end United's hopes of retaining the Premier League title.
Goals from Theo Walcott and Niklas Bendtner gave Arsenal a 2-0 win over Cardiff City to ensure they stayed at the top of the table.
Ole Gunnar Solksjaer, who is coaching Molde in Norway, is expected to replace the sacked Malky Mackay and could be confirmed on Thursday.
Yaya Toure restored City's lead in the 58th with an angled shot into the far corner and Kolarov rifled home in the 66th to secure the points.
Mourinho claimed that Suarez attempted 'an acrobatic swimming pool jump to try to get a penalty' during Chelsea's 2-1 victory over Liverpool.
Roberto Soldado converted his fifth penalty of the season in the first half while Aaron Lennon and Mousa Dembele added goals in the second for a comfortable win.
After Martin Skrtel put the Reds in front from close range at Stamford Bridge after only four minutes, Hazard hit back in the 17th with a superb strike. Eto'o gave Jose Mourinho's team a decisive lead from Oscar's back pass in the 34th.
Romelu Lukaku scored his first goal after five matches to seal a 2-1 win over Southampton at Goodison Park.
The France striker ended a run of seven matches without a goal when he broke the deadlock with a header from Theo Walcott's free kick in the 65th minute.
Borini was substituted at half-time of the match at the Cardiff City Stadium, with Sky Sports reporting that the 22-year-old Italian had subsequently collapsed in the changing room.
The English midfielder made a bet that he would not cut his hair until he next scored a goal. Two and a half years later he finally got an an impromptu pitch-side haircut.
The 34-year-old striker thrust his straightened right arm downwards while tapping his bicep with the other hand after scoring a goal in a game in Britain between his West Bromwich Albion team and West Ham United.