The authority said traffic often tried to switch lanes at the "dangerous junction" on Berkeley Place and Triangle South.
The scheme was financed by a local office development as part of its planning agreement.
Mayor George Ferguson said the changes would be "welcomed by all".
"I don't believe there are many people who drive, walk or cycle in the area who would contest how dangerous that corner is," he added.
The work will take eight weeks to complete.

The fire started at the "A list" Cirque Le Soir venue on London's Ganton Street, just off Carnaby Street at about 04:55 GMT.
Station manager Nic Myatt said: "No-one was inside at the time and there were no injuries." The cause of the fire is under investigation.
Cirque le Soir, a basement venue, describes itself as "London's most A-list club and decadent circus".
Entertainers perform on four stages at the nightclub, a popular venue for celebrities, with minimum spends starting "from as little as Â£100 per head" for a party of 500.
London Fire Brigade said it managed to contain the fire so it did not travel to the restaurant and offices above it.
A Â£95,000 scheme to add a signalled pedestrian crossing to a busy section of road in Bristol will make it safer, the city council has said.
[NEXT_CONCEPT]
More than 50 firefighters have tackled a blaze at a Soho nightclub.