Gertrude was one of six candidates elected in the first round of voting, of which three are women, which has improved the committee's gender balance.
The renowned physicist, who died in March, has had his ashes interred between those of Sir Isaac Newton and Charles Darwin.
The Prime Minister was speaking at a reception in Downing Street last night attended by Sightsavers CEO Dr Caroline Harper.
Journalists from the newspaper visited Uganda to see how the country is tackling this infectious neglected tropical disease, thanks to help from UK Aid.
People aged over 65 can now have a free eye examination while collecting their pension, and can then be referred for treatment for conditions such as cataracts or blinding trachoma.
The election took place during the IDDC general assembly, held in May in Birmingham, UK. Dom has worked at Sightsavers for 13 years and has been a member of the IDDC board since 2015.
More than 4,000 volunteers, most of them women, went door to door with medication to treat the potentially blinding disease.