The use of the implants was stopped in Scotland in 2018 after some women experienced painful and debilitating side effects.
The Scottish Government has now agreed to cover the cost of both the procedure and travel to the private clinics where the surgery can be carried out by specialist Dr Dionysios Veronikis.
Contracts have been awarded to Spire Health Care in Bristol and the Mercy Hospital in Missouri, where specialist Dr Veronikis works.
The surgeon had previously offered to travel to Scotland to carry out the procedure on women suffering because of mesh implants.
But he eventually wrote to former health secretary Jeane Freeman to say the offer had been “permanently withdrawn” after accusing the government of breaking promises and stating that his “goodwill has been abused”.
Announcing the new contracts for private surgery, Scotland’s new Health Secretary Humza Yousaf said: “While mesh removal surgery is available within Scotland on the NHS, these are alternative options for those who feel unable to be treated in Scotland.
“We recognise the pain and suffering of women who have been impacted by complications as a result of transvaginal mesh implants.
“That is why we are absolutely determined to ensure those with mesh complications get the treatment that they want and need.”
It was announced last July that a specialist Complex Pelvic Mesh Removal Service was being set up as part of NHS Scotland, with the Scottish Government committing more than £1.3 million.
But Dr Veronikis had questioned whether women would be willing to be treated at the specialist centre, if they were to be cared for by the surgical teams who had performed their initial operations.
Last month the government also confirmed plans to reimburse the cost of private surgery for women who have already had transvaginal mesh removed.
Such operations cost between £16,000 and £23,000, and the Transvaginal Mesh Removal (Cost Reimbursement) (Scotland) Bill proposes a scheme to reimburse those who have paid for private treatment.