The blue-chip FTSE 100 index (.FTSE) gained 0.5%, while the domestically focussed FTSE 250 index (.FTMC) climbed 0.6%.
The pound jumped 0.8% and government bonds rallied ahead of Hunt's announcement at 1000 GMT, which is expected to detail plans to raise taxes and spend lesser than previously planned.
read more read moreRegister now for FREE unlimited access to Reuters.com Register"The markets have reacted positively to Hunt's expedited timeline, which alleviates some of the fiscal uncertainty," said Victoria Scholar, head of investment at Interactive Investor.
Truss on Friday reversed some of the tax cut measures, and replaced Kwasi Kwarteng with Hunt.
Meanwhile, the Bank of England (BoE) on Friday concluded its emergency bond purchases aimed at supporting the gilts market.