The 47-year-old takes over from Hungarian Laszlo Csaba, who left the Uganda Cranes last July to coach Scottish Premier League club Hearts.
"This has been a great opportunity for us to get a person of Williamson's capability," said Lawrence Mulindwa, president of the Federation of Uganda Football Association (FUFA). "I'm sure he will not disappoint us.
"It was a struggle to select the best of the many good coaches that had applied to work with us in promoting the sport."
Williamson will have a tough task to qualify Uganda for the 2010 CAF Africa Cup of Nations in Angola. The Cranes are scheduled to play Niger and Benin in September and October to be assured their first appearance in the biennual championships since 1978.
The former Scottish striker has coached previously at Kilmarnock, Hibernian, Plymouth Argyle and Chester City.