A 10-year-long deal is due to end in June 2018, and chief constable Andy Marsh confirmed he had "given notice" that the contract will not be renewed.
Instead he said he wants to work with neighbouring police and fire services.
Southwest One, which is 75% owned by IBM, carries out administrative, IT and human resources tasks for the force.
Mr Marsh said: "We will be finding a new way of providing those services. It is my intention to collaborate with other forces.
"I do believe I can save some money and I want to protect frontline numbers."
A partnership with Southwest One was set up between the police, Somerset County Council and Taunton Deane Borough Council in 2007.
The aim was to save about £180m over 10 years.
But in 2012 the private firm launched legal action against Somerset County Council, in a dispute over allegations the firm was failing to deliver promised savings.
The issue was eventually settled out of court the following year with the authority paying a £5.9m settlement.
Somerset County Council subsequently terminated its contract with the company in December last year.
There has so far been no formal comment on Avon and Somerset Police's decision from Southwest One.
Avon and Somerset Police will not be renewing its contract with the joint venture company Southwest One, the BBC has learned.