The championship will be held this year in Cape Town, South Africa, from 3-13 July.
He has been chosen to lead the global organisation until 2018 and is the first British person to hold the post.
The IMO is the world championship of mathematics for students in secondary education and is held in a different country in July every year.
The first IMO was held in Romania in 1959, with seven countries taking part. Today, more than 100 countries take part, representing over 90% of the world's population.
The IMO is the oldest, biggest and most prestigious of all the international science Olympiads and the problems set by the IMO are notoriously difficult.
Dr Smith was elected using "one country, one vote" by the jury of IMO 2014 in Cape Town, South Africa on 8 July. The electorate consisted of representatives of all 105 participating nations.
Participating countries have their own systems of national mathematics competitions, and the UK structure is exceptionally well developed. In the United Kingdom, all the nationwide maths competitions are organised by the United Kingdom Mathematics Trust (UKMT), a registered charity. Dr Smith has chaired the British Mathematical Olympiad Subtrust since 2005, and been Vice Chair of the UKMT since 2013.
The UKMT organises a wide variety of maths competitions, and each year over 650,000 young people participate in Mathematics Challenges (multiple-choice competitions), follow-on competitions (Mathematical Olympiads), and team competitions.
The UKMT also organises mentoring schemes; residential and non-residential mathematics camps; and selection and training of the UK teams to participate in four international mathematics competitions.
As Vice Chair, Dr Smith has helped to address the fact that girls are under-represented in maths competitions at international level. In 2012, he was instrumental in the UKMT launch of the first European Girls' Mathematical Olympiad and this competition now thrives as an annual event, held in a different country each April. UKMT runs a UK talent search for girls each autumn (the "Mathematical Olympiad for Girls") and holds a Mathematics Camp for Girls in the University of Oxford during the summer.
Dr Smith said: “I am very grateful for this endorsement from the worldwide mathematics enrichment community. I aim to serve both the International Mathematical Olympiad, and to promote maths competitions more generally.
“Maths competitions play a key role in stimulating interest in mathematics, and driving up intellectual standards both in the developed and developing world.
“The IMO sits at the apex of a pyramid of maths competitions in over 100 countries, and provides a focus for intellectually talented young people from all cultures to test themselves with a spirit of friendly but intense competition.”
Dr Smith was awarded an MBE for Services to Education in the Birthday Honours list in 2011 and has has been a UKMT volunteer since 1999.