The scheme will add a new route for pedestrians and cyclists, aiming to make it easier for people to travel in more sustainable ways.
The council said the changes to the junction will reduce congestion, improve bus journey times, provide safer crossing facilities and help to support “economic growth across Leeds and Bradford”.
Some bus stops will also be affected by the works, with the lane closure due to end on 17 October.
Councillor Jonathan Pryor, Leeds City Council’s deputy leader and executive member for economy, transport and sustainable development, said: “We thank everyone for their ongoing patience while we continue to work hard at Dawsons Corner.
“We have done lots of work to try and minimise the disruption these works will create, but whatever the amount of planning there may be some delays.”