“Real Sociedad have reached an agreement with David Moyes to be the coach of the first team until June 30, 2016,” Sociedad said in a statement published on their website.
“Tomorrow (Tuesday) the details for his official presentation and the backroom staff led by the Scottish coach will be finalised.”
Moyes was sacked in April after less than a season in charge of United as they failed to qualify for the Champions League for the first time since 1995.
The Scot enjoyed a broadly successful 11-year spell at Everton prior to taking the job at Old Trafford, although he has yet to win a major trophy as a coach.
Sociedad have been looking for a new boss since Jagoba Arrasate was sacked last weekend after just one win in their opening 10 league games.
However, they responded in style to beat La Liga champions Atletico Madrid 2-1 on Sunday to move out of the relegation zone.
Sociedad have a history of appointing British managers as John Toshack enjoyed three spells as boss in San Sebastian, whilst current Wales manager Chris Coleman had an ill-fated six months in charge during the 2007-08 season.