AC Milan manager Carlo Ancelotti, new Manchester City boss Mark Hughes and former Inter Milan boss Roberto Mancini had been in the running for the job but the appointment ends weeks of speculation after Grant was sacked towards the end of May.
The Chelsea statement continued: "Scolari gets the best out of a talented squad of players and his ambitions and expectations match ours. He was the outstanding choice.
"Out of respect for his current role and to ensure minimum disruption to this work there will be no further comment from Chelsea nor from Felipe about his new role until his employment with us commences.".
Paulo Ferreira said he would be happy to see Scolari at Chelsea
Scolari has long been the nemesis of English football as he was in charge of both Brazil and Portugal when they ended England's chances in the 2002 World Cup, Euro 2004 and the World Cup in 2006.
His reputation led him to be considered for the England manager's job in 2006 but he was reportedly put off the role because of fears of media intrusion.
However, with his contract with the Portuguese Football Federation set to expire on 29 June - the date of the Euro 2008 final - he has taken the opportunity to try his hand at management in the Premier League.
The former defender has never managed a European club but has won the Copa Libertadores - South America's equivalent of the Champions League - with Brazilian clubs Gremio and Palmeiras.
He has also won a Brazilian championship (Gremio) in 1996, three Brazilian cups and three South Rio Grande championships.
LUIZ FELIPE SCOLARI FACTFILE
1948: Born Passo Fundo, Rio Grande do Sul, November 9
2001: June - Replaces Emerson Leco as Brazil coach
2002: May/June - Brazil win the World Cup for a fifth time
2002: December - Takes over as Portugal manager
2004: Portugal lose to Greece in final of Euro 2004
2006: Pulls out of the running to succeed Sven-Goran Eriksson as England manager
2006: Leads Portugal to World Cup semi-finals
2007: Linked with England job for a second time but again vows to see out Portugal contract
2008: June - Confirmed as new manager of Chelsea, taking over on 1 July
Speaking before the appointment, Portugal and Chelsea defender Paulo Ferreira said: "We need a good manager and Scolari is a good manager. He can do a good job (at Chelsea) and he will be good for the club."
And former Chelsea player Gavin Peacock believes Scolari, known as 'Big Phil' because of his authoritarian management style, could make the Blues the entertaining team chief executive Peter Kenyon is looking for.
"You can't argue with his record," Peacock told BBC Sport. "If you're looking for someone with charisma and presence in the dressing room, then he is your man.
"His teams play with flair so it fits in with what Chelsea say they have been looking for but the everyday involvement, getting into the players' minds, will take time.
"I suspected he might be lined up when Chelsea signed Jose Bosingwa last month and there was talk of Deco coming to the club."
However, he warned that Scolari's lack of English could make things difficult for the Brazilian.
"My only question mark would be about his level of English. Does he speak it?" said Peacock.
Someone like the England manager Fabio Capello didn't speak it but he had time to learn and he has time between each England gathering, but Scolari will need to get his ideas across every day. It will be a challenge.
"For example, Mourinho, on his first trip away with the team for a pre-season friendly in the United States, sat on the plane with Joe Cole for two hours just getting to know him. Scolari will not be able to do that sort of thing."
Match of the Day pundit Alan Shearer, meanwhile, speculated on how Scolari's appointment might affect Cristiano Ronaldo's decision whether to stay at Manchester United.
The interesting thing for me now is does Cristiano Ronaldo go to him for advice on where he should go?
Match of the Day pundit Alan Shearer
The Portugal winger has been heavily linked with Real Madrid and Shearer told the BBC: "The interesting thing for me now is does Cristiano Ronaldo go to him for advice on where he should go?
"Does he stay in England or go to Spain? I know what Scolari's advice to him might be now!"
Alan Hansen added: "I think its a very good choice. If you're going into that dressing room you've got to have one, a presence - he's got that - and two, a great track record, and he's got that as well.
"He's got the right credentials and he's done fantastically well with Portugal. The big players will find you out in a minute and a half, so it's a great choice."
Scolari's first competitive game as Chelsea manager will be the first Premier League match of the 2008-09 season on the weekend of 16-17 August.
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