The strategically located island in the eastern Mediterranean, a former British colony, was split after a Turkish invasion in 1974 triggered by a brief Greek-inspired coup.
For the first time in more than a decade, Greek and Turkish Cypriots plan to submit maps to the United Nations detailing their proposals on territorial boundaries between constituent states in a two-zone federation.
“I welcome the continued courage and commitment that has been shown by both sides,” Johnson said in a statement. “The talks in Geneva on the Cyprus settlement offer both sides a unique opportunity to find a solution.”
Britain was willing to help in any way it could, he added.
Representatives from Greece and Turkey are also expected to join the talks on Thursday.
The three countries are guarantor powers of the independence of Cyprus, allowed to intervene to restore constitutional order under a 1960 treaty.
“I hope that all those involved will approach the talks with a sense of openness and flexibility. I believe that if approached in this light, a solution is in reach to bring lasting peace to Cyprus,” Johnson said.