They said the country’s new self-declared leader, Capt Ibrahim Traoré, had Lt Col Paul-Henri Damiba’s resignation and conditions he had set.
The announcement followed attacks on French institutions, after it was reported that Lt Col Damiba was sheltering at a French military base.
It is the second coup this year.
In both cases, the country’s dire security situation and failure to deal with an Islamist insurgency were blamed for the takeovers.
Burkina Faso controls as little as 60% of its territory, experts say, and Islamist violence is worsening.
The African Union has demanded the return of constitutional order by July 2023 at the latest, agreeing with the regional group Economic Community of West African States (Ecowas) that the ousting of leader Lt Col Damiba was “unconstitutional”.
Ecowas earlier said it was “inappropriate” for army rebels to seize power when the country was working towards civilian rule.
No statement has been released by Lt Col Damiba directly.
But religious and community leaders said Lt Col Damiba himself had offered his resignation “in order to avoid confrontations with serious human and material consequences,” according to quotes cited by AFP news agency.
They said Lt Col Damiba had set seven conditions for stepping down – including a guarantee of his security, an agreement to continue with efforts at national reconciliation and a continued respect for the guarantee of returning to civilian rule within two years.
The deposed colonel had himself ousted President Roch Kaboré in January, saying that he had failed to deal with growing militant Islamist violence.
Many citizens in Burkina Faso have not felt safe for some time.
The Islamist insurgency broke out in the country in 2015, leaving thousands dead and forcing an estimated two million people from their homes.
Burkina Faso has experienced eight coups since independence in 1960.
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