Granada name former Arsenal captain interim boss
Granada lie 19th in La Liga, seven points adrift of safety with just seven games remaining.
Adams has been working as an advisor at the Spanish club as part of his role with DDMC, a Chinese football management company tied to Granada owner Jiang Lizhang.
"The club puts all its confidence in Tony Adams, vice-president of DDMC, as first team coach until the end of the season," Granada said in a statement.
Sunday's 3-1 home defeat to Valencia prompted the relegation-threatened club to pull the plug on Alcaraz's third stint as Granada coach.
"After evaluating the situation the team is in and the performances that the team has shown in the last few games, Granada CF has decided to bring to an end Lucas Alcaraz and his coaching staff's time as head of the first team," the club added.
Adams becomes Granada's third coach of the season after Alcaraz replaced the sacked Paco Jemez in October.
The 50-year-old won four English league titles as a player at Arsenal but has struggled in previous managerial spells at Wycombe Wanderers, Portsmouth and most recently with Azerbaijani club Gabala.
Much of the blame for Granada's poor form has been aimed at the club's Chinese owners and a chaotic recruitment policy.
Their 25-man squad contains 16 loan players from 18 different countries.
However, Adams says his role is to bring stability and a more Spanish core back to the club.
"I am here to put the Spanish structure in place, with players belonging to Granada CF fighting for Granada," he told the club's website last week.
"We inherited 106 players, of whom only 44 actually belong to Granada.
"Our aim is to return Granada CF to Granada so the people here can identify fully with their team and their players."