In a bid to save money and reduce bureaucracy for teachers, he is also introducing a new survey assessing only literacy and numeracy which replaces the Scottish Survey of Achievement.
The SSA was introduced in 2005 to assess pupils in P3, P5, P7 and S2 in English language, maths, science and social subjects. Its successor will assess only literacy and numeracy in P4, P7 and S2 in alternate years.
Although Scotland will continue to participate in the Organisation for Economic Co-operation and Development's Programme for International Student Assessment (PISA), regarded as the "gold standard" of international surveys, it will withdraw from PIRLS, which studies progress in reading and literacy among 9 and 10-year-olds across 35 countries, and TIMSS, which looks at trends in maths and science for pupils aged 9-10 and 13-14 across 50 countries.
Mr Russell said: "Participating in three different international surveys doesn't provide value for money in the current economic climate and can lead to wasteful duplication. I am therefore proposing that we follow the lead of the other devolved administrations."
A spokesperson for the Scottish Government said its withdrawal from PIRLS and TIMSS would save more than pound;800,000 and "significantly reduce the burden on schools".
Mr Russell added: "Clearly, we will always need robust and comprehensive information on how the Scottish education system is performing. However, we also know that collecting statistics places a burden on headteachers and teachers, meaning they have to fill in forms and collate information. This type of bureaucracy is not helping our schools, pupils or teachers."