Premier Barry O'Farrell said the jobs would be in new government offices and would boost western Sydney's economy.
He said the government would seek expressions of interest for 5000 square metres of commercial space in each of the three centres, which equates to between five and 10 storeys in additional office space in each.
"The NSW government will not own the new office accommodation but will instead become an anchor tenant for new investment," Mr O'Farrell said.
He says the move "makes economic sense and has the added benefit of ensuring that public servants are based in the communities they serve".
A spokesman for the Premier said the Community Relations Commission and divisions within the Family and Community Services would move from Sydney's CBD and Ashfield to Liverpool.
"Relocation will begin as existing office leases are approaching renewal," the spokesman said.
He said he could not confirm how many of the 3000 jobs would be going to Liverpool.
"Individual agencies are still consulting with their staff," the spokesman said.
"Exact numbers have not yet been finalised.
"However, staff will be relocated in accordance with their conditions of service."
Liverpool mayor Ned Mannoun said he was "over the moon" about the announcement.
"It's a wonderful achievement, which we've all been working towards for a long time and I'd like to thank Menai MP Melanie Gibbons in particular, because she was always in the ear of the Premier," he said.
"Not only is this great news in terms of jobs it will bring directly to the region but it will also act as a catalyst for further commercial development and send a strong signal to investors."
Ms Gibbons said the relocation would provide more opportunities for Liverpool residents to work closer to where they live and would bring lots of life to Liverpool's city centre.
Source: Liverpool City Champion by Anne Tarasov. Original article.