Israeli Grant, previously director of football, will have a baptism of fire when they Blues face Manchester United at Old Trafford on Sunday.
"The club is delighted that in Avram we have an experienced man who can come in immediately at this difficult time to help deliver our objectives.
"In Steve we have a Chelsea man and he will be a crucial part of the management team going forward.
"Avram and Steve have our full confidence and support."
Meanwhile, Mourinho paid a visit to Chelsea's training ground at Cobham on Thursday morning before leaving at 10.45am.
The Portuguese raced past a flock of reporters and photographers, declining to comment on his exit before being driven off.
