Itineris won the account after a competitive pitch against two other digital marketing firms.
The agency has been tasked with creating a site that will educate and inform visitors about the charity's work and encourage people to donate.
Jean Jones, head of fundraising at The Leprosy Mission, said: "Our existing website had been up and running for around six years but had become dated and not engaging for visitors.
"We are confident that itineris was the right agency to work with. Even at pitch stage, the team understood our vision and were able to translate this into design concepts, which offered a much needed feeling of freshness and vitality."
Itineris will also assist The Leprosy Mission with email marketing.
The is due to switch to the new design in early October.