Middlesex, are currently in Antigua, competing in the Stanford Super Series where they lost by 12 runs to England on Sunday.
Chief executive Vinny Codrington, said in a statement: "We haven't finalised everything yet, Angus has gone on holiday and we're in Antigua and we expect to sign contracts when we get home
"As it became fairly public knowledge we wanted to confirm that he's the man we want and that we have agreed terms with Gus to start the role in January.
"Gus is Middlesex through and through and we'll be very fortunate to have him.
"Middlesex are moving away from the old-fashioned committee style and getting somebody to be responsible and accountable for everything in relation to cricket.
"It's not a tracksuit job, it's not about being in the first-team dressing room and it's not going to step on (coach) Toby Radford's toes, but Gus is going to be ultimately responsible for everything that is Middlesex cricket, from first-team to grass roots."
Former England off-spinner Shaun Udal, on Fraser's recommendation, has been offered the captaincy of the club.
Udal, 39, spent the bulk of his career with Hampshire before joining Middlesex at the start of last season having briefly retired from the first-class game because he couldn't get into the south coast county's Championship side, which at the time was captained by Shane Warne.
However, by the time the Australia leg-spin great decided not to see out the final year of his contract, Udal had already made the move up to London.
Middlesex were one of the dominant sides in the English county game throughout the 1980s and early 1990s but their success last season in winning the Twenty20 Cup was their first major honour for 15 years.
"It is an unbelievable honour to captain this great and proud club and it is my intention to return it to its glory days of years gone by," said Udal.
"I have been fortunate to have achieved a few things in my career but this is right up there with my proudest moments.
"I also applaud the choice of Gus Fraser and look forward enormously to working closely with him."
Fast-medium bowler Fraser, now 43, played 46 Tests for England between 1989-1998, taking 177 wickets at 27.32.
Having spent the whole of his 18-year first-class career with Middlesex, he retired in 2002 to become the cricket correspondent of Britain's Independent daily newspaper while also pursuing a career as a broadcaster.