The universities and science minister will recommend to the Privy Council that the institutions have met the criteria to be awarded the title.
It follows the government's decision to lower the threshold for university title from 4,000 full-time higher education students to 1,000 students.
The applicants being put forward to the Privy Council for formal approval are: Arts University College at Bournemouth; Bishop Grosseteste University College Lincoln; Harper Adams University College; Leeds Trinity University College; Newman University College, Birmingham; Norwich University College of the Arts; Royal Agricultural College; University College Birmingham; University College Falmouth and University College Plymouth St Mark & St John.
Mr Willetts said: "These well-known and highly-regarded university colleges represent over 1,200 years of history between them. It is right to remove the barriers preventing high-quality higher education providers like these calling themselves universities simply because of their size.
"I am delighted that they have taken up the opportunity offered by our reforms. This will lead to the biggest creation of universities since 1992 and will enable more people to realise their aspiration of going to a university."
All 10 new institutions are members of GuildHE, which lobbied the government to make the change in the threshold for university title.
Andy Westwood, chief executive of GuildHE, said: "The minister's recommendation that 10 institutions have met the criteria to become universities recognises the quality, diversity and tradition that they bring to UK higher education."
Peter Lutzeier, principal of Newman University College, said that "the university college title did create confusion outside the sector. The clarification provided by obtaining full university status is particularly important in light of the recent marketisation of higher education and will prove invaluable as we look to strengthen our international links."
The announcement follows the news last week that the privately-funded College of Law would become the University of Law after successfully applying through Companies House to use university title.