The Conservative-led authority made the announcement as part of plans to save Â£55m during 2011-12.
The council, which has nearly 15,000 employees, plans to save Â£7m by cutting senior management, freezing recruitment and renegotiating contracts.
Liberal Democrat councillor Keith House said the council was in "financial chaos" after it failed to plan ahead.
The Winchester-based council employs about 40,000 people.
Excluding teaching staff, who will not be affected, there are 14,990 people in 11,182 full-time posts.
The cuts represent about 8% of the workforce.
It has blamed the cuts on a reduction of Â£30.9m (14.3%) in its government grant, following the Spending Review.
Peter Terry, of public sector Unison, called the cuts "unnecessary" and said strike action could not be ruled out.
"It's quite devastating news for us, for the staff who work for the county council and for the communities that rely on the council's services," he said.
"This council has decided upon itself to roll out four years of cuts into two.
"It's a double whammy and has been made twice as bad for the people of Hampshire."
Mr House, leader of the council's opposition, said it was "unrealistic" for the council to blame the coalition government
"It should have been obvious to the council leadership way before the election that there would be some devastating times ahead," he added.
"They should have planned ahead.
"Residents are going to see that some services are going to stop and others will get worse, across the country, month by month, more and more will change."
Jane Frankum, the council's only Labour councillor, said the authority had chosen to "cut deeper and faster" than was really needed.
Council leader Ken Thornber told the BBC he expected "anxious months" of talks with unions.
He reassured residents budgets for child protection, highways maintenance and schools will be protected.
Council tax will also be frozen at last year's levels.
"One could point the finger at the last government who spent money that it was going out of style and we could point the finger at the bankers," he told the BBC.
"But quite frankly, what I have got to do is to take what the government say should be our reduction and work to it.
"I don't remember in 30 years of service anything remotely like the difficulty we are in at the moment."
The budget is expected to be approved by the full council on 24 February.
Union bosses said 1,200 job losses at Hampshire County Council would lead to "inferior services" to communities.