Balfour will design and construct a 2.5m stretch of busway along the Aston Vale to Temple Meads section under a contract worth £26m.
The dedicated busway follows former rail routes and will feature a new bridge over the Bristol to Portishead rail line.
Balfour Beatty will start designing the busway this month with main construction due to start in June and be finished by October 2016.
Welsh contractor Alun Griffiths has won the £19m contract to design and construct the second section of the guided busway known as the South Bristol link.
This will run around the south and west of Bristol city centre between the A370 Long Ashton Bypass and Hengrove Park.
Griffiths beat two other shortlisted bidders in a hotly contested race against Costain and Graham Construction.
Kier has picked up a £6m contract on this route to build a railway under bridge at Parson Street.
The Government has confirmed funding packages to supplement the first two major sections and a decision is expected in March on the final third section known as the Northern Fringe to Hengrove package, which completes the circuit.
The West of England Partnership – an alliance between the four councils in Bristol, Bath, South Gloucestershire and North Somerset – is understood to have selected a preferred bidder but a contract will not be signed until full funding is agreed.
Several other packages are also up for grabs on separate bridge elements along the guided busway. The biggest package at £13m involves building a new overbridge at Stoke Lane onto the M32.
A further five contracts will involve two new bridges and three upgrade and strengthening jobs to listed bridges on the city centre route worth together around £10m.