Banks involved in the venture include Barclays, HSBC, Lloyds Banking Group, Royal Bank of Scotland, Santander UK and Standard Chartered.
It is thought Welton will become the chief executive of the fund, while Sir Nigel Rudd will become the fund's chairman.
The fund has been dubbed a new 3i and will invest in companies with a turnover of £10m to £100m.
It is part of the Project Merlin agreement between Britain's biggest banks and the government, announced last week.
Under the scheme banks will make up to £190bn available for UK business customers, with another £76bn earmarked for SMEs.
