Lynn raced for Jaguar during the second half of the 2018/19 season following the departure of Nelson Piquet Jr. from the team.
The Briton scored a best result of seventh, which was one position lower than his best ever FE result of sixth, which he achieved the season before with DS Virgin Racing.
"I am excited to be rejoining the Jaguar Racing team and returning to Formula E," said Lynn.
"I am familiar with the championship, the team, their goals and how they work. I look forward to playing my part in helping the team achieve their objectives."
However, it is not yet known if Lynn will replace Calado, as he too has a drive at the WEC round.
Jaguar team principal James Barclay said: "Mitch Evans and James Calado are an exciting combination and they will be strongly supported by Alex throughout the season.
"Alex is not only a very talented and accomplished driver, he also has valuable experience in Formula E and a great relationship with our team.
"That experience and relationship will be highly beneficial to our ongoing development. Winning races can only be achieved if you have a hard-working, talented team around you. Bringing Alex back into the fold helps us achieve that."
Bahrain International Circuit - Winter testing