In his August 18 letter to the Speaker of Parliament, the president also appointed Justices Paul Mugamba and Richard Buteera to the Supreme Court bench.
"This is, therefore, to forward to you their names and Curriculum Vitae for parliamentary approval," the president concludes his letter.
The letter is copied to the Prime Minister, Minister of Justice and Constitutional Affairs and the Chairperson of the Judicial Service Commission.
If approved by Parliament, Justice Owiny-Dollo will replace Justice Steven Kavuma who retired in April having served in the position for two years.
In May last year, Justice Owiny-Dollo convicted seven men behind the July 11, 2010 terror attacks in Kampala that claimed the lives of 74 people.
The double bombing targeted two venues the Ethiopian Restaurant and Kyadondo Rugby Club as revelers watched the World Cup Final match between Spain and the Netherlands.
Five of the convicts were sentenced to life imprisonment while the two received 50 years each. Thirteen others were acquitted.
It was the calm demeanour with which Justice Owiny-Dollo handled the highly sensitive case that endeared him to many. The men could have faced the death penalty, the maximum for terrorism, but Owiny-Dollo said he did not believe it would act as a deterrent.
_URN