It said Mr Russell would lead the Scottish government's negotiations with Westminster over "our future relationship with the EU".
Mr Russell has been given the title of Minister for UK Negotiations on Scotland's Place in Europe.
He has previously held the environment, culture and education briefs.
But he has been out of the Scottish cabinet since Nicola Sturgeon replaced Alex Salmond as first minister in November 2014.
Ms Sturgeon said the appointment, which is subject to approval by Holyrood when it returns next month, was an indication of the importance she was placing on the negotiations.
She added: "We already have an agreement with the new prime minister that the Scottish government should be fully involved in the development of the UK government's position ahead of Article 50 being triggered and beyond, and that options to protect Scotland's relationship with Europe will form part of these discussions.
"By putting a dedicated and experienced minister at their centre, it will ensure that Scotland's voice is heard loudly and clearly. I am confident that Michael Russell will make strong and constructive representation to the UK government throughout this process."
The first minister said External Affairs Secretary Fiona Hyslop and Europe Minister Alasdair Allan would continue to lead discussions with EU institutions and member states.
She added: "Derek Mackay will continue to have overall responsibility for the constitution, including overseeing preparations for a new independence referendum bill should that prove to be the best or only way to protect Scotland's interests."
Mr Russell was previously Minister for Environment from 2007 until 2009 and then served as Minister for Culture, External Affairs and the Constitution before moving to the role of Cabinet Secretary for Education which he held until November 2014.
He said he was "delighted and honoured" to accept the new role.
He added: "Following the overwhelming vote in Scotland to remain in the EU, it is essential that Scotland comes together to defend our national interest. Accordingly in these discussions, it is important that the nation speaks, as much as possible, with one voice.
"I will therefore want to listen and learn from the widest range of individuals, communities, organisations and companies about their hopes and fears for the future."
Mr Russell, who will report directly to the first minister, is expected to attend the second meeting of the EU Standing Council next week.

Pre-tax profits dropped to £49m from £53.5m in 2014.
But the Cardiff-based society - the largest in Wales - said it had helped 3,500 first-time buyers onto the housing ladder, up by 1,200 on the previous year.
It also warned 67 workers at its Nemo secured loans business that they were at risk of redundancy.
It has been trying to offload Nemo and said it would no longer take on any new customers.
However, the building society said it believed it could find jobs for many of the staff within its 1,000 strong workforce.
Meanwhile, Principality, which is the sixth biggest society UK-wide, said mortgage lending to home-buyers had passed the £5bn mark for the first time.
Graeme Yorston, group chief executive, said it had been "another strong 12 months".
He said the society would continue to respond to technological demands, which have included rolling out mortgage interviews on Skype and online appointment booking.
Underlying profit was £57.8m, up from £51.9m.
This included dealing with one-off issues like stopping new lending from its subsidiary Nemo, which provides secure loans on properties.
There has been speculation over recent years that Principality would look to sell this part of its business.
It will continue to manage accounts it currently has.
Mr Yorston said although Nemo had made a £14m profit, it did not want to "increase our participation in this market".
Looking ahead at economic prospects, he said he did not expect to see any rise in the official Bank of England base rate until 2017 and "when it does it is likely to be modest".
Michael Russell has been appointed as the Scottish government's new minister with responsibility for Brexit negotiations with the UK government.
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Principality Building Society has announced a dip in its profits for 2015, after a record the year before.