Tuesday's decision follows years of uncertainty and disputes between all parties involved in the course, which is owned by East Lothian Council.
Internal issues at Musselburgh led to the British Horseracing Authority stepping in to demand an independent governance review - which then resulted in the council deciding to bring in a third-party operator.
Musselburgh has been operating under a temporary licence from the BHA, which had been due to expire on October 15. However, the governing body last week agreed to extend it to the end of the year as the process dragged on.
Chester Race Company is being invited to sign an initial 10-year contract.
East Lothian Council leader Willie Innes said: "This is a very welcome announcement, which secures the future of Musselburgh Racecourse.
"The facility has earned an excellent reputation thanks to the hard work and commitment of its employees - and one which we have always been keen to maintain and support.
"Appointing a third-party operator was one of the options set out in the independent governance review required by the BHA. The working group unanimously agreed that this was the most appropriate option to pursue.
"Chester Race Company is recognised as a leader in its field and, through the procurement process, has demonstrated that it has the expertise to take Musselburgh Racecourse forward."
Chester chief executive Richard Thomas said: "We are delighted to have been successful in the tender process. It has been our long-held ambition to increase the number of racecourses within our group, and this is just the start of that process.
"It is fantastic to now be able to say we have three racecourses spanning the British Isles.
"Musselburgh is a fantastic course at the heart of the East Lothian community, and we are committed to ensuring its future is protected. We are excited to get started by working closely with the team and driving a successful handover."
After the conclusion of a standstill period, which follows the procurement process, Chester Race Company will be invited to sign the initial 10-year contract to operate the racecourse on the council's behalf.
A date for the start of the new contract has yet to be confirmed.
Musselburgh general manager Bill Farnsworth believes the transfer of racecourse operations to Chester promises a bright future for the course.
He said: "We are delighted Chester racecourse have been appointed as the preferred new operator - and its well-established reputation of providing high-quality racing, for supporting owners and trainers and offering a five-star visitor experience for racegoers are all values which chime strongly with the team at Musselburgh.
"The preferred new operator can be assured they are inheriting a fully committed, talented and ambitious team who want Musselburgh to succeed and to retain its position as one of the UK's leading smaller racecourses.
"We are excited about being part of this next chapter in Musselburgh's 200-year plus history - and with Chester's support, we can ensure East Lothian will remain a top destination for the country's leading race horse owners and trainers.
