Police in Leicestershire, Nottinghamshire and Northamptonshire will instead form a "strategic alliance" to coordinate their work.
A spokesman for the Unison union said the decision was "good news for our members and the public".
A full alliance, which was "not a merger", could be in place by 2020.
A police spokesman from Northamptonshire said "a decision was made not to progress any further work by G4S across the three forces in this area".
Leicestershire Police and Crime Commissioner Sir Clive Loader said: "We'd prefer to be the masters of our own destiny."
A spokesman for the three forces said: "On 3 November, we announced that G4S had been asked to carry out a feasibility study into contact management.
"We are grateful to G4S for providing their report but although we have identified an urgent need to explore options... we can confirm at this early stage that this will not include outsourcing.
G4S spokesman John Shaw said the firm was "disappointed" that a deal had not been agreed.
"We firmly believe that we can help police forces unlock resources in their support functions to release money for front-line policing and keep more officers on the beat."
A joint statement from the three forces' police and crime commissioners said: "To be quite clear, the alliance is not a merger.
"It is all about protecting the quality of local policing services in each force area as a result of maximising efficiencies ... and each force will retain its own identity."
Leicestershire Police Unison branch secretary Chris Hanrahan said the union will be looking to meet chief police officers early next year to discuss the three-force alliance.
Three police forces who looked at handing over their 999 control rooms to the private sector have decided not to go ahead with a deal.