The 50% shares previously not under Fairfax’s ownership were acquired from co-founder Paul McGonigle for an undisclosed sum.
The transaction involves Fairfax exiting Positive Lending, the master-broker he co-founded with McGonigle in 2009.
Fairfax takes full control of Catalyst, which has provided over £250m of short-term funding to date and has a loan book exceeding £100m.
The business, which is being funded by a combination of institutional and private capital, will launch into new markets later this year.
Sam Freeman, partner of Laceys Solicitors advised Arlan Holdings, the acquisition company wholly owned by Fairfax, and McGonigle was advised by Charles Frank, partner at Keystone Law.
Fairfax said: “I am absolutely delighted to have completed the acquisition of Catalyst.
“After spending over a decade as a specialist finance broker, I launched Catalyst by compiling everything I learned from working with other lenders, good and bad, to create a business I would have loved partnering with as an intermediary.
“I believe truly understanding the intermediary perspective and my broad experience of the market are key reasons as to why Catalyst has experienced the amazing growth trajectory to date.
“Looking to the future, we will continue to serve short-term mortgage customers and intermediaries well, and we look forward to expanding to other areas of property lending over the coming months.
“I would like to thank Paul for his contribution to date and I wish him well for the future success of Positive Lending.”
