The Amy Poehler and Aziz Ansari comedy series was on US broadcast net NBC in the US where it ran to seven seasons. In the UK it has previously been on BBC Four.
The ensemble comedy, set inside a parks planning office, is distributed by NBCUniversal International Distribution, which struck the Dave deal.
It gives the UK digital channel seasons four to seven of the series for the linear Dave channel as well as its catch up service UKTV Play.
The first two of the four seasons will start in late July and the latter two from summer 2016.
Alexandra Finlay, head of acquisitions for UKTV, said: “We’re delighted to extend our partnership with NBCUniversal on this deal. As an award-winning comedy with a superb cast, Parks and Recreation is a fantastic addition to Dave’s scripted acquisition slate.”