The bus lane, introduced as an experimental measure, will run for 430 metres from the Rodney Place junction in the west to St Saviour's & St Olave' School near Bricklayers Arms in the east.
TfL says: "Alongside benefits for buses and bus users, the new bus lane can provide an improved facility for cyclists in the absence of formal cycle infrastructure and support sustainable growth as significant development is expected in the area over the next few years."
Works to paint the new road markings will take place overnight this week.
Once the work is completed, the new bus lane will be operational 24 hours a day.
The bus lane trial will last for up to 18 months and TfL has create an online survey to collect feedback.