The future of Frank Burrows, who acted as caretaker manager following Megson's departure, remains uncertain.
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Megson has previously managed Norwich, Blackpool, Stockport and Stoke before arriving at West Brom.
Megson twice achieved promotion to the Premier League with West Brom, in 2002 and 2004.
Trotters boss Gary Megson suggested the Reds could well win the title this season.
Gary Megson was then appointed but stayed just six weeks before taking over as manager of Bolton Wanderers.
Former Bolton and England midfielder Reid has been tipped to replace Gary Megson, who was sacked on Wednesday.
Former West Brom boss Megson, 48, has been out of work since leaving Nottingham Forest in February 2006.
Megson is expected to take charge of Bolton in time for Sunday's Premier League match against Aston Villa.
"The crowd's reaction to me towards the end wasn't particularly palatable from my point of view, " Megson said.
However, Megson defended the decision to take off Klasnic, who is on a season-long loan deal from Nantes.
Gary Megson's side had earlier seen a header from Helguson sail over and Guthrie shoot wide when unmarked inside the area.
He becomes the Foxes' fourth permanent boss of 2007 following spells under Rob Kelly, Martin Allen and Gary Megson.
Megson left for the Premier League post after just six weeks in charge.
But the result was that Megson had to be thrifty in the market.
Did he give Megson any real chance of building on Big Sam's success?
And Megson is quick to acknowledge that his team have "a difficult run-in".
Gary Megson's side took a 1-0 lead into the second leg and restricted the strong Spanish side to few chances.
Mandaric revealed that it was after the game that Megson requested a meeting with the Foxes chairman about his future.
Paul Jewell, Graeme Souness and Chris Coleman were all linked with the post before Megson emerged as the surprise favourite.
And most of all the fact that Megson lost twice the number of league games that he won in 2009.
"The manager Gary Megson has bought some experience players this summer and I definitely think it's going to help, " he added.
Bolton boss Gary Megson made moves for a replacement for Nolan on Monday, when he signed midfielder Mark Davies from Wolves.
Before being appointed by Leicester on 13 September, Megson had been out of work since leaving Nottingham Forest 18 months earlier.
But Gary Megson's side took the lead when Morgan bundled in from close range at the second attempt after 29 minutes.
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Megson managed the Potters back in 1999 and also worked under Pulis as an unpaid coach for three months at the club.
But Frank Burrows, who had been in temporary charge along with Taggart after Megson quit to join Bolton last month, has left.
Megson will be the Foxes' fifth manager in 18 months and the fourth since Milan Mandaric took control of the club in February.
Megson succeeds Martin Allen as Foxes boss, with ex-Leicester defender Gerry Taggart and Frank Burrows to be given roles in his coaching staff.
Before his spell at the City Ground, Megson had also managed Norwich, Blackpool, Stockport and Stoke before a four-year reign at West Brom.
And on the back of five games unbeaten, Southgate is keen for the Teessiders not to drop that record against Gary Megson's side.
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