"gradually rolling out" is correct and usable in written English.
You can use it to describe a process that is taking place over a period of time. For example, "The company is gradually rolling out a new product line across the country."
The scheme was revealed in January, and has been gradually rolling out since then.
The bank is gradually rolling out the new site to customers in randomly selected groups, so not all customers will see the new version immediately.
DugDug focuses on dogs, but will be gradually rolling out other pet categories like cats, birds, fish, reptiles and small pets (including ferrets, guinea pigs, gerbils etc).
The new service will be gradually rolling out for iOS and Android devices and will be set to complement the streaming service's Discover function which offers music recommendations to users based on past listening habits and other algorithmically-scrubbed data.
Sainsbury's has been gradually rolling out similar efficiency measures across its estate, with the result that its water consumption is now 50% lower (on per square metre basis) than in 2005/06.
Emails are gradually rolling out to reservation holders.
Apple wants to do it all at once rather than gradually start rolling out a few DRM-free tracks here and there.
Up until now, the chat functionality was completely ad-free, but now Fring will gradually start rolling out banner display ads, beginning with a small number of randomly selected users.
Mr. Sterling attributes Yelp's success to its young, urban demographic, as well as to starting in San Francisco and entering other markets gradually, rather than rolling out nationally all at once.
This technique was gradually superseded by rolling out mats of pre-tamped clay, and in turn by the development of geotextile linings in the mid twentieth century.
An ART intervention was incorporated by gradually rolling-out ART among infected persons with CD4+ cell count less than 200 cells/μl and reaching full coverage by 2020.
