The move comes at a time many African leaders are trying to cling on to power by extending their time in office.
The electoral commission said 63% had approved the changes proposed by President Macky Sall. Turnout was 38%.
The opposition have criticised Mr. Sall for failing to cut his current tenure – the changes take effect in 2019.
The leaders of countries such as Burkina Faso, Burundi, Rwanda and Congo sought to extend their rule last year.
Such moves have triggered violent protests in Burundi and Congo.
The new constitution proposes 14 other changes, including:
- Limits the age of presidential candidates to 75 and allows independents to run
- Reaffirms the limit to two presidential terms
- The opposition leader will have a status recognised by the constitution and will enjoy official benefits
- Local councils get more powers
- New rights for citizens – to a healthy environment and over natural resources and land ownership