It will buy Motorola Solutions shares at $68.50 each, with the whole amount coming to roughly $1 billion.
Motorola said in a statement it will use the money to develop products for video monitoring, analytics and content management.
Back in April, Motorola Solutions put itself up for sale but no one was interested in taking it to the altar.
Motorola Solutions is nothing to do with Motorola Mobility, which Chinese firm Lenovo now owns.
Silver Lake staff were the masterminds behind turning Dell into a private company in 2013.