Sammy Lee has been confirmed as the new manager of Bolton Wanderers.
Lee was Allardyce's assistant for almost two years
Lee, 48, takes over at the Reebok Stadium after the shock resignation of former boss Sam Allardyce on Sunday.
"I'm delighted about the prospect of being Bolton manager," said Lee. "It is a great legacy that Sam has left and it is my job now to carry that forward."
Lee, who became a coach at Bolton in June 2005, added: "It took me one second to decide to accept the job after it was offered to me."
To go from fifth to fourth place in the Premiership isn't another £10m, it's about £100m
Bolton chairman Phil Gartside
It is Lee's first job in management after a successful coaching career with Liverpool, England and Bolton.
"I am very proud to be sat here in front of everybody as the new manager of Bolton Wanderers," he stated.
"The education I've gained from working with Sam Allardyce has been immense.
"I have to continue what Sam has started, that's first and foremost, and then re-evaluate it after that.
"It certainly is a healthy position that Bolton are in, we're now contesting for a place in Europe.
"The main thing for us is to keep the players stable and to make sure that we get the result we firmly feel we deserve after all the hard work we've done this season."
Trotters chairman Phil Gartside poured cold water on media reports that Allardyce left the club because of a lack of funds being made available in the summer.
Gartside said: "There has been speculation about funds.
"But if you look at where Bolton are in the Premiership and where they have been over the last few years, there must have been some funds available.
"Look at last summer, when we brought in a world-class striker in Nicolas Anelka and Abdoulaye Meite too, so I would like to put it on record that funds have been available.
"However, to go from fifth to fourth place in the Premiership isn't about another £10m, it's about £100m.
"We work within our resources and it is based on what we can afford to put in."
Gartside also denied speculation that Allardyce has got another job lined up after being linked with Manchester City and Newcastle United.
"Sam told me he hasn't got another job," insisted Gartside.
SAMMY LEE FACTFILE
Born 7 Feb 1959
Won three league titles, two European Cups and four League Cups for Liverpool
Won 14 England caps
Began coaching career in 1993 as reserve team boss at Liverpool, before becoming first-team coach under Gerard Houllier in 1999
Joined Sven-Goran Eriksson's England coaching staff in 2001
Became assistant manager at Bolton in 2005
Turned down full-time England Under-21 coaching job in 2006 and quit international set-up to concentrate on Bolton
"But today is about Sammy Lee being appointed manager. I respect Sam's views of why he has left.
"You couldn't look back on the last eight years without a lot of enjoyment and pride. We've taken Bolton Wanderers to a level we've never been at before.
"Now I'm looking forward to a different era. It is not a complete surprise. When Sam had a great chance of getting the England job a year ago we talked about what we could do then."
Allardyce quit as Wanderers boss on Sunday after eight years at the helm.
On Monday he revealed he had timed his resignation to allow "the team and Sammy to focus on the last two games without any speculation".
He added: "I'd have liked it to be the end of the season, but unfortunately some things don't stay private.
"It wasn't to be because all the speculation would have carried on. We decided yesterday was a good time.
"It's time for Sam Allardyce to take a break. I've made one of the biggest decisions I've ever made, and once I make it, I stick to it."