The 30-year-old has turned down the offer of a new contract with last year's champions and has been given permission to open talks with other counties.
Hampshire are emerging as the favourites to sign him but there are certain to be other offers for him as well.
Mullally, recovering from a shoulder injury ahead of the winter tour to South Africa, said: "I am leaving on amicable terms. I have had 10 great years here but nothing lasts forever and we have come to the end of an era.
"It is not all about money and on many, many occasions in the past I have turned down offers to go elsewhere for more money than Leicestershire would have paid me because I wanted to be part of a side heading for success.
"But I have not enjoyed my cricket here as much this year and, although Leicestershire offered me a contract, they didn't exactly bend over backwards to keep me."
Mullally could be followed out of Grace Road by the wicketkeeper Paul Nixon, who is also out of contract at the end of the season and has yet to agree a new deal.
Darren Bicknell is to leave the county champions Surrey to re-establish his career. The elder brother of opening bowler Martin has not been able to gain a regular place in the side this summer, though the opening batsman scored two hundreds - against Somerset and Sussex - in his limited appearances.
"I've not had a regular place in the side for the last three seasons," said the 32-year-old.
"I want to be playing in all competitions at this stage of my career. Our squad is strong and I'm unlikely to get that chance."Reuse content