Following design work by Network Rail, Government proposals involve building a new £10.63 million station at Reston and a new £11.13m station at East Linton.
The local authorities have now written to Transport Minister Humza Yousaf confirming their support for an option to include the new stations in a programme of works covering Edinburgh and the South East of Scotland.
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Scottish Borders Council will provide £2.84m to help build the station at Reston, while East Lothian will allocate £3.44m for East Linton.
It is estimated the stations will be operational by 2021.
Cllr David Parker said: "Both councils believe the proposed approach gives certainty about the stations' delivery.
"We believe the package is a significant step forward and we await the Minister's positive response.
"Data this week from the Scottish Tourism Economic Assessment Monitor has revealed how the Borders Railway is beginning to provide significant economic and social benefits for the central Borders, and we believe the re-introduction of a station at Reston could do the same for residents in the east of our region."
(LM)
