Former Australia fast bowler Jason Gillespie, the coach of county champions Yorkshire, heads the favourites to be appointed to the fulltime role.
Both Strauss's appointment and Moores's exit had been widely tipped in the British press and were announced in successive ECB statements on Saturday.
Moores has now lost the job of England coach on two occasions, having initially been fired from the post in 2009 after a bust-up with then captain Kevin Pietersen.
His second spell in charge, which came after he replaced Andy Flower following the team's 5-0 Ashes thrashing in Australia in 2014, lasted barely a year.
It yielded just one series win, at home to India last year, and included England's embarrassing exit from the World Cup, where they failed to beat a single Test side.
Afterwards came the recent 1-1 series draw in the Caribbean against a West Indies side labelled "mediocre" by incoming ECB chairman Colin Graves.
"At the moment it's difficult to put into words how I feel except to say how disappointed I am in the way my term as England coach has ended," said Moores in the same ECB statement that announced his exit.
"I will walk away knowing I've given my all to the role and always put the team at the front of any decision making," added Moores, whose tenure concluded with Friday's washed-out one-day international away to Ireland in Malahide.
-AAP