The Meffan Institute in Forfar will be one of the museums to close on Mondays.
The opening hours of several Angus museums will change in April for the first time since the 1980s.
Monday closures will be the norm at the Signal Tower Museum in Arbroath, Brechin Town House Museum, the Meffan Institute in Forfar, Kirriemuir Gateway to the Glens Museum and Montrose Museum.
The local authority said this is in line with opening patterns for other UK and European museums and delivers budget savings.
Neighbourhood services vice-convener Jeanette Gaul said trial runs of different hours had not been effective.
She added: “A pattern of five-day consecutive opening from Tuesday to Saturday, 10am to 5pm, with no lunchtime closure seems to be the best arrangement to meet the needs of visitors to the museums.”
The Signal Tower Museum will also continue to open on Sunday afternoons in July and August.
