He made the announcement after visiting the college which was set up in 1997 and known then as United College Sarawak (UCS) at the Old Airport Road here.
Early this year, the Sarawak Foundation took over its running at the invitation of its board of management.
It was renamed Kolej Laila Taib in memory of the late Datuk Amar Laila Taib, wife of Chief Minister Tan Sri Abdul Taib Mahmud, for her contribution to the development of education in the state.
Najib said he had very long been a strong supporter of the state.
"When I was Education Minister, I gave the licence to set up the Curtin University branch campus in Miri. Then, I was persuaded to give a licence for the Swinburne University branch campus in Kuching.
"Today, I am presented with another request, that is to elevate KLT to university college in 2012.
"On behalf of the federal government, I have agreed to this on the basis of merit," he said.
Najib said now that the government had fulfilled the request from the people of Sibu, it was for them to then fulfil his request, referring to the coming Sibu by-election.
Meanwhile, he said it was vital to provide quality education to the young so that they could assist in the nation-building process and in its transformation programme.
He said there was one aspect of his 1Malaysia initiative which had not been talked about often but was equally important.
"This is to build Malaysia into a 21st Century Nation with global competitiveness.
"We need to provide for, nurture and retain all talents we can develop in the country to allow us to do this," he said.
Later when visiting the re-building project of the SRK St Mary here, Najib announced a government grant of RM1 million for its construction fund.
The state government had earlier given a grant of RM600,000.
The school, built in 1954, is one of the oldest wooden mission primary schools in the state.
Its rebuilding project was initiated by the late Sibu member of parliament and Deputy Transport Minister Datuk Robert Lau Hoi Chew who died on April 9 in Kuala Lumpur.
Taib in his speech said KLT would focus on training more technical and management manpower needed for the successful implementation of the state's regional development corridor or SCORE (Sarawak Corridor of Renewal Energy).