This was revealed to KickOff.com by Chiefs' team manager Bobby Motaung.
"We spoke to Sheffield over the weekend and we have agreed on a deal for the player. They said they faxed me the signed agreement today after signing it, but I haven't seen it. I'm waiting for it," Motaung tells KickOff.com.
However, the Zimbabwean international, who was close to signing for English club Queens Park Rangers just over a week ago, has very little time to finally fulfill his dream of playing in England.
Today is the last day of the transfer window and a work permit application could be a stumbling block.
"They were also trying to arrange his work permit and I don't know if they got it. For now I'm waiting for their fax and I will get back to you," Motaung adds.
The left back had secured a work permit after he was offered a three-year deal by Portsmouth, but Chiefs blocked the move when they said the player still belonged to them after exercising a year option in his contract, though Bhasera's been disputing it, saying his contract expired last June.
When Portsmouth pulled out of the deal after the matter was referred to Fifa, Bhasera started training with Queens Park Rangers, where he had apparently impressed but left to go train with Sheffield, where he also impressed.
Motaung says if Sheffield secures a work permit, Bhasera could be their player by the end of today.