"has gradually grown into" is correct and usable in written English.
You can use it to describe how something has become more prominent or popular over time. Example: The popularity of the restaurant has gradually grown into the most renowned spot in town.
Commercial litigation finance began in the late nineties and has gradually grown into a three-billion-dollar industry dominated by big banks and hedge funds.
The 21st century Education has gradually grown into an environment or field of communication that has broken the edge of limitations to information dissemination.
Relationships you assume would last but has gradually grown into a tumor that needs to be cut off otherwise could be damaging, the replacements are on its way but first you had to be put in a position where you will not take for granted or hesitate to embrace a rare opportunity.
With the progressive aging of the population, osteoporosis has gradually grown into a global health problem for men and women aged 50 years and older because of its consequences in terms of disabilities and fragility fractures.
Mohammed Sadiq Mamdani, director of the Al-Mizan, says demand has gradually grown since they started in October last year.
Both have ciliated larvae that gradually grow into juvenile worms rather than passing through a morphologically distinct larval stage.
Milan, who qualified for the final as runners-up to Juve in last season's Coppa Italia, had struggled up until that point but they gradually grew into the game as their opponents failed to build on the early breakthrough.
Therefore, the molybdenum nanowalls have a polycrystalline part in the bottom and gradually grow into a crystalline structure at the top end.
I would have to slowly work my way up to such a style, gradually growing into a new wardrobe, the way women gradually grow out of a bad haircut and into a better one.
Guardiola had chosen Phil Foden for a second start in the competition and he gradually grew into the contest.
