Allardyce took charge earlier this season after Slaven Bilic's exit, but could not keep the Baggies from getting relegated - and has now confirmed he will not be in charge following the conclusion of this season.
The former England manager will be joined by assistant Sammy Lee and first-team coach Robbie Stockdale in departing the club, leaving Albion with the task of recruiting a manager ahead of the Championship campaign.
Allardyce signed an 18-month deal when he replaced Slaven Bilic in December.
But that contract included a break clause which allowed Albion or Allardyce to end their agreement early if the club was relegated from the Premier League.
Albion had offered Allardyce the chance to remain as boss, but the 66-year-old decided against staying on.
In his own statement, Allardyce confirmed his decision and explained the reasons behind the decision.
"West Bromwich Albion made me a generous offer to stay at The Hawthorns that shows the commitment of an ambitious club. After serious consideration I have decided not to accept that offer." he said.
"If I were to stay and achieve promotion next season the expectation would be for me to continue for at least another season and, sadly, that is not a commitment I feel able to make at this stage of my career."
"I believe the club now needs stability and continuity and this would, in my opinion, best be provided by a young and ambitious manager who can get us back to where we should be as an established Premier League football club.
"I must thank the players and staff, in particular Luke Dowling and Ken (Xu Ke), for their unwavering commitment to a very difficult challenge during my time at the club. This challenge was made all the more difficult, of course, by the enforced absence of the club’s fantastic supporters, some of whom I am delighted were present for our final home game against West Ham United.
"The club have asked for my opinion on the qualities my successor will require and I have been more than happy to offer my thoughts. The search for my replacement starts after the final game of the season at Leeds United. In the meantime, we will be concentrating fully on the preparation for that game and will do everything we can to finish the season with as many points as possible."
Sporting Director Luke Dowling issued his thanks to Allardyce, admitting that he and chief executive Xu Ke had hoped the boss would be willing to remain in charge as the club hoped to battle for promotion.
"Sam, Sammy and Robbie came in at a really difficult time for the football club and worked tirelessly in their efforts to keep the club in the Premier League." he said.
"Unfortunately, collectively, we were unable to achieve our goal of surviving relegation. In the second half of the season we played with passion and desire, delivering some memorable results with organised, entertaining football.
"Ultimately, we were unable to accumulate the points total required to keep us here, but Sam certainly restored pride with a number of resilient displays.
"Sam, Ken (Chief Executive, Xu Ke) and I have discussed at length our plans for the future and we very much hoped to have Sam in charge for next season and beyond.
"Sam and his coaching staff have been excellent to work with and I would like to thank them all for their efforts.
"Sam has given his reasons for leaving and we respect his decision. He has been brilliant to work with and I wish him, Sammy and Robbie all the very best in the future. They will always be welcome at The Hawthorns.”
The club will now start the process of finding a replacement for Allardyce, with the boss set to take charge of his final game away at Leeds this weekend.
Former Sheffield United boss Chris Wilder is the overwhelming early favourite for the soon-to-be vacant role, at 4/6, with ex-Albion assistant Graeme Jones joint-second favourite with Frank Lampard at 14/1.