Mowbray returns to Celtic Park after playing for the club in the 1990s
Celtic have confirmed Tony Mowbray as their new manager after a deal was concluded with West Brom.
Mowbray arrives from the club relegated from the Premier League in England along with assistant Mark Venus and first-team coach Peter Grant.
Present Celtic coach Neil Lennon will remain as part of the Scottish Premier League club's management team.
Mowbray, who becomes the 16th manager of Celtic, will speak at a media conference at 1000 BST on Wednesday.
The Glasgow club at the weekend agreed to pay the £2m in compensation demanded by West Brom, with a Celtic source insisting that it would not reduce money available for new players.
Boyd hails attacking Mowbray style
West Brom were seeking further compensation for Venus and Grant, while there were question marks about the role of Lennon, who had been previously been given assurances by Celtic chief executive Peter Lawwell.
Mowbray had been one of three managers targeted by Celtic, along with Burnley's Owen Coyle and Swansea's Roberto Martinez.
Burnley's compensation demand appears to have been what thwarted Celtic in their desire to talk officially to Coyle.
Celtic then turned their attention to Mowbray after Martinez was approached by Wigan.
Mowbray played for Celtic between 1991 and 1995, straddled by spells with Middlesbrough and Ipswich, with whom he started his coaching career.
He had a brief spell as caretaker boss at Portman Road after the sacking of present Scotland boss George Burley before becoming a manager in his own right at Hibernian.
He is obviously aware of Celtic and he will be well received by the fans
Association of Celtic Supporters' Clubs secretary Peter Rafferty
Mowbray led the Edinburgh club to two top-four finishes in 2005 and 2006, after which he left for West Brom.
He led the Baggies to the Championship play-offs, losing to Derby, but the following season they won the title and promotion to the Premier League.
However, they only lasted a season in England's top tier and were relegated, despite receiving plaudits for their attacking style of football.
Mowbray's appointment will also result in a return to Celtic Park for Grant, who spent 15 years with the Glasgow club.
Grant, who began his coaching career as assistant boss at West Ham, spent a year as manager of Norwich before joining Mowbray at West Brom in 2008.
West Brom chairman Jeremy Peace had been determined to keep Mowbray - and refused to back down over his claims for compensation.
"Tony leaves with our best wishes for a successful future in football," Peace told the club website.
"We will now concentrate fully on the important task of appointing a new manager who can take the club forward.
"As we stated last week, we did not want to lose Tony nor did we encourage Celtic's approach.
"However, there was a compensation clause in Tony's contract which has been met to our satisfaction and, after talks with Celtic, Tony has decided to join them."
Speculation has already begun as to who Mowbray's first signings will be and Peace may have a battle on his hands to prevent his former manager returning to plunder his squad.
West Brom captain Paul Robinson has been quoted as saying he would like to follow Mowbray to Celtic Park, while another left-back, out-of-contract Real Sociedad player Xabi Castillo, is apparently keen on moving to Celtic.
Midfielder Borja Valero and striker Marc-Antoine Fortune, who was on loan from Nancy, have also been linked with a move to Celtic Park from the Hawthorns.
Mowbray's appointment had already been welcomed by Celtic fans, according to Peter Rafferty, secretary of the Association of Celtic Supporters' Clubs.
Celtic fans react to Mowbray appointment
"He has served a decent apprenticeship in Scotland and England," he stated. "He is obviously aware of Celtic and he will be well received by the fans.
"Peter Grant will be coming with him and nobody is a bigger Celtic man.
"Even at West Brom Tony was committed to playing good football and the fans still supported him - and that says a lot when he got the team relegated."
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