Elash and Aboody established MTF in 2008 and the firm has since successfully completed more than £1bn of lending.
The MT Finance Group raised £8m of funding from Triple Point Investment Management to complete the purchase.
The option contract was signed in November with the transaction needing to be completed before the Budget on 3 March.
Earlier this year the lender launched a regulated bridging proposition with products available up to 65 per cent loan to value (LTV).
Co-founder Elash said the buyout was the start of a new and exciting chapter for the business.
“We wish to express our gratitude to the teams at Triple Point, EY and Ashurst for their tireless assistance, day and night, in getting this done under the tightest of time constraints,” he added.
Reece Digance, relationship director for leveraged finance at Triple Point Investment, added: “We are excited to partner with MT Finance to support the buy-out.
“It was clear to us from the outset that MT Finance’s customer proposition is first class, supported by technology, customer service, and speed of execution. We look forward to supporting the business’ ambitions in the near future.”
Nick Parkhouse, partner at EY, added: “We have worked closely with Joshua and Tomer for a number of years and we are delighted to have advised MT Finance on the buy-out.
“This transaction was completed entirely remotely and demonstrates the continued strength and attractiveness of the underlying MT Finance platform.
“We share the company’s excitement about the future and this transaction will enable the team to act on the sizeable opportunities that are available to them.”