The bridge consists of two pairs of braced steel beams which are 36.26m long and each weigh 70 tonnes.
The work took place at the weekend when traffic flows are 20% lower than on an average weekday.
To reduce the need for further closures, Highways England carried out survey work at Eastville viaduct whilst the MetroBus bridge works were carried out.
Mark Driscoll, emergency planning manager for Highways England, said: “We’re pleased to say that the messaging and communication proved effective ahead of the weekend closure, and motorists were able to plan their journeys into and out of Bristol while the MetroBus bridge was installed over the M32.”
These new bus priority measures will mean that some bus journeys between UWE, Bradley Stoke and the city centre will be up to 30 minutes quicker than existing bus services.