Outerwall Inc., known for its Redbox movie rental kiosks and Coinstar coin counting machines, agreed Monday to be taken private by Apollo Global Management for about $900 million.

Apollo will acquire Outerwall, which is based in Bellevue, Wash., for $52 a share, a transaction value of $1.6 billion when including debt, the companies said in a statement.

As more consumers opt to stream movies or rent them “on demand” directly from cable providers, Outerwall’s D.V.D. rental business has suffered. The company’s stock price plummeted between July 2015 and February, after a few years of declining revenue growth. Outerwall’s chief executive, J. Scott Di Valerio agreed to step down in January 2015, with a director, Nora M. Denzel taking over in the interim. Outerwall appointed Erik E. Prusch as chief executive one year ago.

The management turnover and depressed stock price encouraged an activist investor, Engaged Capital, to acquire a 14 percent stake and agitate for the company to sell itself or pursue other options to turn itself around. Engaged, led by Glenn Welling, settled with Outerwall in April, obtaining one board seat immediately and the right to name two additional directors by August.