The striker re-joins the Clarets for a second spell after two seasons away from the Melbourne Community Stadium.
Shaun, 27, started his youth career with Coventry City, before breaking into the first-team to make 8 senior appearances between 2008-2013. During his time with the Sky Blues, Jeffers spent time out on loan at Cheltenham Town, Cambridge United and Tamworth.
He also earned 2 international caps with the England Under-19's.
After leaving Coventry, he went on to feature for the likes of Peterborough United, Newport County and Yeovil Town, gaining plenty of Football League experience.
Shaun first signed for Chelmsford City in August 2016 after leaving Yeovil Town. He struck a fierce partnership with fellow striker Shamir Mullings before the latter departed in the November of that season for Forest Green Rovers.
Jeffers went on to make 52 appearances during the 2016/17 season, scoring 24 goals.
His fine form that season earned him a move to National League side Boreham Wood the following summer and also joined Hampton & Richmond Borough on loan towards the end of 2017/18 season. He helped Hampton reach the Playoff Final of that season, eventually losing to Braintree Town on penalties.
Shaun signed for Brackley Town ahead of the 2018/19 season, making 16 appearances, scoring 6 goals.
Discussing his return, Shaun said:
"I'm happy to return to a Club where I had great success. Hopefully we can go one better next season and get promoted.
"I've worked well with the Management Team and the Club before and Chelmsford still has a place in my heart. I can't wait to get started."
Welcome back to Chelmsford, Shaun!