The former Yorkshire and England all-rounder has been on the coaching staff at the Ageas Bowl since 2012, holding positions as assistant coach and bowling specialist, before becoming head coach in 2016.
Morley-born White led Hampshire to their first trophy in six years by winning the Royal London One-Day Cup in 2018.
“I’ve had a fantastic six years at Hampshire and I’m proud of what we’ve been able to achieve as a group in that time,” said White, who was brought up in Australia before returning to play for the White Rose between 1990-2007.
“While it has certainly been a tough decision for me to make – and one that hasn’t been made lightly – spending long periods of time away from my family has become more and more difficult.
“I feel that now is the right time to return to be with them on a more permanent basis.”
Hampshire’s director of cricket Giles White praised the dedication of the outgoing head coach, saying: “We understand his decision to step down and have been aware of the difficulties of being away from his family.
“On behalf of the club I’d like to thank Craig for all the hard work and incredible contributions during his time here, he will be missed on both a personal and professional level.”
Leicestershire spinner Callum Parkinson has signed a contract extension to keep him at the club until the end of the 2020 season.
The 22-year-old emerged as a regular in all formats for Paul Nixon’s side, and took 26 wickets across the three competitions last season.
Parkinson, brother of Lancashire’s Matt, struggled with the red ball but enjoyed success in the NatWest Blast with 15 victims, and Nixon is hoping he can continue to progress after extending his stay at Grace Road.
“Parky (Callum Parkinson) is a talented young spinner who works tirelessly on his game,” said Nixon.
“He is a versatile performer who will continue to mature.
“I played with a brilliant left-arm spinner in Claude Henderson, who went on to get better and better as his career developed.”