A source close to the deal said Sir Brian's vehicle, Souter Investments, had taken a stake of more than 30% in the business, which was part of the Alexander Forbes Group. The sources said: "This is a bigger stake than normal. They see this as a really good investment."
The proposed deal was first announced in August but has now received clearance from the Prudential Regulatory Authority.
It is understood that Sir Brian, founder and chairman of bus and rail group Stagecoach, is attracted by the ambitious growth plans of the management team at Mobius Life, which is on track to double its assets to more than £4 billion in the course of this financial year.
Sir Brian said: "We are delighted to support Mobius Life and its management team as it continues its growth.
"We expect this to continue into the future as a strong, independent business."
Mobius Life, which is named after the mathematical object the Mobius strip, advises pension schemes on investment platforms.
Mobius chief executive Adrian Swales said: "As an independent business, Mobius Life will continue to provide clients with the outstanding service and bespoke solutions they are used to, with the comfort of complete independence and the support of committed UK financial backing."
Souter Investments' other interests include Scottish bus maker Alexander Dennis and homecare provider Baywater Healthcare.