The 27-year-old will replace Chris Moyles, who announced his departure from the programme after eight years earlier this morning (July 11).
"I'm super excited to be hosting the iconic Radio 1 Breakfast Show," Grimshaw said. "It's been a dream of mine since the age of 11 and to be honest it hasn't really sunk in yet.
"I love Chris and have always looked up to him as one of the best broadcasters ever."
Digital Spy music editor Robert Copsey and Sugarscape editor Kate Lucey react to the news:
Radio 1 controller Ben Cooper added: "Nick is a great broadcaster with a passion for music and a mischievous sense of humour, which has made him a hit with our listeners.
"He will be an excellent host for Radio 1's new breakfast show, bringing a new generation of listeners with him."
His appointment was revealed at around 10.30am by Fearne Cotton, who said she was "very, very chuffed" for Grimshaw but would "miss Moyles a lot".
"He's a dear friend of mine," she said. "He's just going to have a great time. He is free to do what he pleases."
Grimshaw, who joined the BBC in 2007, will be the 17th DJ to front the Breakfast Show in Radio 1's 44 years on air.
He currently presents a two-hour late night show from Monday to Thursday and occupies the 10pm-midnight slot on Sundays alongside Annie Mac.
Photo gallery: Radio 1 Breakfast Show DJs through the years:
Copyright: PA Images PA Archive
The T4 host won the role over the widely-tipped Greg James, who inherited the Drivetime Show from Scott Mills, another of Radio 1's most prominent DJs, in April this year.
Grimshaw's appointment has been seen as a reflection of Cooper's vow to attract more viewers under the age of 30 to the station.
Moyles, who is the longest-serving Breakfast Show host, will step down from the programme in September. He is contracted to stay at Radio 1 until 2014.
"Radio 1 are going to find someone new to host the show and they'll put their take on it," he said in an on-air statement. "Radio 1 can do that when they want to do that but this show is all about me and it's all about the team.
"With the hope of sounding over the top and melodramatic I wanted to say thank you to everybody listening to the show for giving the team and me the best time ever."