The 23-year-old has joined for an undisclosed fee and signed a two-and-a-half year deal with Rovers after completing a successful trial in November.
And May says he was impressed enough by his time in South Yorkshire to opt for a switch to Doncaster, with several league clubs chasing his signature.
He said: “From the minute I met the players, they came out of their way to ask where I was from and introduce themselves.
"It made it so much easier and took a lot of weight off my shoulders.“It is a big step, but I feel confident I can play in League Two and training every day will only improve me.“I’ve done really well in non-league with Hythe, I’ve felt they’ve really got the best out of me.
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"But working with Darren Ferguson as manager is different – I reckon he can get goals out of me too.”
May started his final game for Hythe on Saturday but failed to add to his 22 goal tally for the season.
Hythe play in the Ryman League Division One South, level eight of the English football pyramid, equivalent to Evo-Stik Division One South.
Though May is making a significant jump in standard, Rovers boss Darren Ferguson feels he has signed a natural goalscorer.
"Alfie’s got good potential," Ferguson said.
"There are a lot of things I like about him, mostly his attitude.
"He’s got an absolute desire to be player and that was the real thing for me.
"The level he’s been getting goals at is obviously nowhere near what he is coming into but he is a natural goalscorer.
“He had a week with us in November and it gave us a chance to look at him and give him a chance to look at us.
"His club Hythe has been excellent in terms of managing his situation, and his manager has too, in terms of letting us do that."
It is a sentiment shared by Hythe boss Clive Cook.
He said: “Alfie now has the opportunity to realise his dream and I know he will take it with both hands.
"He is a smashing lad, easy to manage, easy to get on with and thoroughly deserves to go into full time football. I am sure he will succeed there.
“Alfie came to Hythe Town 16 months ago after I took the job as manager and the first thing that came to my mind was what an incredible talent he has.
"He has made 67 appearances for us scoring 49 goals, a fantastic return at any level of football.”
“Other Football League clubs were interested but Doncaster were quickest off the mark, so I would like to thank them for giving Alfie the opportunity to realise his ambition to be a professional footballer.
"That’s what he wanted and that’s what he has got through hard work, talent, dedication and honesty.”
May's signing is the second piece of business for Rovers on the first day of the January transfer window after it was confirmed Jordan Houghton's loan spell from Chelsea has been extended.