The loss of the mandate comes just two months after Schroders lost the mandate to manage the £303m Schroders UK Growth trust to Baillie Gifford.
The Omnis UK Equity fund is available exclusively to advisers that are part of the Openwork Group.
The Schroders duo of David Docherty and Andy Brough had run the fund, with Mr Docherty the lead manager since 2016.
Over the past three years to 6 June the Omnis fund has returned 20 per cent, compared with 24 per cent for the average fund in the IA UK All Companies sector in the same time period.
This performance left the fund ranked 195th out of 259 funds in the IA UK All Companies sector in the same time period.
The fund will now be run by the UK Equity team at Franklin Templeton, which is lead by Colin Morton.
The team is based in Leeds.
They run the £513m Franklin Templeton UK Equity Income fund, which has returned 30 per cent over the past three years to 6 June, compared with 20 per cent for the average fund in the IA UK Equity Income sector in the same time period.
Toni Meadows, chief investment officer at Omnis, said: "We see the team at Franklin Templeton as offering a genuine core approach to investing in UK equities, having also built a formidable reputation of expertise in medium and smaller company stocks; this is a real stand-out feature compared to rival managers in the UK equity sector, and we think they will do an excellent job managing the Omnis UK Equity fund."
A spokesman for Schroders said: "We have an excellent, long standing relationship with Omnis and work with them on a number of funds. Whilst we are naturally disappointed with this decision we look forward to continuing to work with them in the future."
The change takes effect from 11 June.
Darius McDermott, managing director at Chelsea Financial Services, said Mr Morton is one of the longest serving UK equity income managers around and has a sold track record.
He added that Mr Morton tends to focus on large caps almost exclusively, which Mr McDermott said is now rare among the equity income managers in the UK.