The lender stopped accepting new mortgage applications from existing customers at the beginning of April as it moved to a new platform.
Initially the direct product transfer service was supposed to be back up and running in May, but the return was delayed as the bank suffered an IT meltdown in April.
Mortgage customers who lost out by staying on the lender’s Standard Variable Rate (SVR) will be refunded the difference in interest payments, TSB has pledged.
The lender plans to extend product transfers to brokers as soon as it can.
TSB results last month revealed the IT crisis had cost £176m, and mortgage lending had taken a hit during this time.
The lender advanced £2.6bn of new mortgages in the six months to the end of June, down from £4.1bn in the same period last year.
However, total customer lending over the period was £31bn, up 2.8% year-on-year.
A TSB spokesperson said: “We can confirm that our product transfer capability for customers is available.
“Customers can now easily transfer to a new mortgage deal when their current offer is coming to an end.
“Customers wishing to a complete a product transfer with TSB can do so by contacting their local branch or by calling us on 0800 056 1088.”