Two free schools were approved by the Department for Education, to provide 120 extra primary school places next year, building to a total of more than 800.
Bellevue Place Education Trust was given the green light to open Richmond Bridge Primary School from September 2015, with an intake of 60 pupils before eventually growing to 420 places.
The Gems Learning Trust has also been given the go-ahead to open a school of the same size, Twickenham Primary, next year.
Councillor Paul Hodgins, Richmond Council cabinet member for children's services and schools, said: "Given the huge and ever-increasing demand for places at our primary schools, I would like to offer my congratulations to the two successful free school applications.
"Richmond primary schools are heavily oversubscribed and these two new schools will add four new forms of entry, and an additional 120 reception year places and will ease the strain in the east Twickenham areas that will have a particular shortfall."
Joint deputy leader of the Liberal Democrats Councillor Gareth Roberts said: "While I'd like to congratulate Gems and Bellevue Place, the Tories must be breathing something of a sigh of relief as they'd pretty much bet the farm on these two schools opening.
"They were fortunate that when they took control of the council in 2010 they inherited a fully costed primary expansion strategy from the previous Lib Dem administration; a strategy so good they've spent the past four years claiming credit for it but they didn't learn from previous mistakes and had nothing planned beyond 2014, so this is a massive lifeline for them."
Both organisations will now work together with the Education Funding Agency to identify sites for their schools.