The ICC Board will now begin the process to identify Allardice's successor.
Bilic took over the reins at West Brom in 2019 and was tasked with gaining promotion from the Championship to the top flight.
Sam Allardyce has been named England manager on a two-year contract, the Football Association said in a statement on Friday.
England squad members received postcards from Sam Allardyce saying their 'journey has just begun' on Thursday, two days after his short reign as manager was brought to an abrupt end, according to British media reports.
Sam Allardyce was sacked as England manager on Tuesday having behaved "inappropriately" when seeking a lucrative sideline role while talking to undercover reporters, bringing a crushing end to his dream job after one match and 67 days in charge.
'As a group we need to stick together and concentrate on the football. The other side is not our issue'
England manager Sam Allardyce has defended the decision to leave Everton midfielder Ross Barkley out of his first squad for the 2018 World Cup qualifier in Slovakia at the weekend. The 22-year-old has enjoyed an impressive start to the Premier League season and many observers felt he had done enough to deserve a place in the 23-man group named on Sunday.
England football team manager Sam Allardyce has been caught up in a newspaper sting in which he is alleged to have met a bogus consortium of Far East businessmen seeking advice on the Premier League's billion pound transfer market.
Former Bolton Wanderers and Newcastle United manager Sam Allardyce took charge of troubled Blackburn Rovers on a three-year contract on Wednesday.
England captain Wayne Rooney has welcomed the appointment of Sam Allardyce as national team manager and confirmed he is not planning on retiring from international football after the country's disappointing showing at the European Championship.
Sam Allardyce is the obvious candidate to replace Roy Hodgson as England manager if the FA decide to go with a home-grown candidate for the job, former Manchester United boss Alex Ferguson has said.
Sam Allardyce was sacked because his football vision did not fit in with that of Blackburn Rovers' new Indian owners who believe the club should be fourth or fifth in the Premier League.
Blackburn Rovers manager Sam Allardyce became the second mid-table Premier League manager to be sacked in eight days after the club's new Indian owners announced his departure with immediate effect on Monday.
New manager Sam Allardyce said the days of talking about England's potential are over and it has to become reality as he looked ahead to qualifying for the 2018 World Cup.
New England manager Sam Allardyce believes it is just the right time in his career for him to be taking on what some have called the impossible job.
Sunderland named David Moyes as their new manager on Saturday, replacing Sam Allardyce who was appointed as England manager.
West Ham United manager Sam Allardyce has signed a new two-year contract at the Premier League side, the east London club's co-owner David Gold said on Twitter on Saturday.
West Ham United manager Sam Allardyce believes it is acceptable for players to "make a meal out of" contact if it helps them win penalties and free kicks.
Sam Allardyce got off to a flying start as manager of Blackburn Rovers when the Premier League strugglers beat Stoke City 3-0 on Saturday to claim only their second home victory of the season.
Defender Gary Cahill has said he is ready to prove his worth to new England manager Sam Allardyce to retain his place in the national team. The 30-year-old, who has 47 caps for England, was regularly picked by former manager Roy Hodgson and was part of the squad that suffered an embarrassing defeat by Iceland in the last 16 of the Euro 2016. "I'm looking to keep involved and keep that shirt. I am excited to be working under Sam," Cahill told British media. "I'm looking to impress him at the start of the season and also if I'm fortunate enough to be involved in the squad.
News of all that's transpired on and off the football field.
West Ham United manager Sam Allardyce deserves credit for re-introducing the 'West Ham way' after a positive start to the Premier League season, co-chairman David Sullivan said on Friday.
West Ham United appointed Sam Allardyce as their new manager on Wednesday, the Briton succeeding Avram Grant, who was sacked following the London club's relegation from the Premier League.
Bolton manager Sam Allardyce has called on world soccer's governing body FIFA to scrap new guidelines on the offside rule.
Leeds sack Gracia, Allardyce to step in till season ends
Over the course of the next two years, the former England international was able to engineer a turnaround in fortunes for the team, leading them to the 2018 World Cup semi-finals before their run to the final of the Euro 2020 tournament last year.
Should Manchester United win their next two games, the gap will be cut to four points and while only a collapse of astonishing proportions would deny Manchester City the title.
An emotional and apologetic Sam Allardyce said on Wednesday an error of judgement had led to his shock exit as England manager following a newspaper sting.
Sunderland have given permission to the Football Association (FA) to speak to manager Sam Allardyce about the vacant England post, the Premier League club said on Wednesday.
British police said on Friday they had opened an inquiry into an allegation of bribery following a review of a newspaper's investigation into suspected soccer corruption.
City's Guardiola defends Mendy after COVID protocol breach.
Sunderland manager Sam Allardyce will seek divine intervention ahead of Sunday's clash with Premier League leaders Leicester City after watching his relegation-threatened side fail to convert dominance into goals last weekend.
Images from the English Premier League matches on Saturday.
News of all that's transpired on and off the football field
The Football Association (FA) have urged the Daily Telegraph to provide "full and unfettered disclosure of all available material" following allegations of corruption by the newspaper.
A summary of Saturday's action in the Premier League.
Sunderland manager Sam Allardyce reckons Atletico Madrid boss Diego Simeone would be labelled boring for his defence-oriented style if the Argentine were managing a Premier League club.
West Bromwich Albion secured a stunning 5-2 win over 10-man Chelsea at Stamford Bridge
West Ham United's teenage defender Daniel Potts was taken to hospital suffering from concussion after being briefly knocked out in a second-half clash of heads with Arsenal defender Bacary Sagna in their Premier League match on Wednesday.
Speaking at a news conference in Newcastle, his club manager Sam Allardyce said the striker had suffered a torn thigh muscle and also had a suspected weakness in his stomach area which may require surgery.