The 19-year-old will go straight into the squad for Saturday's home clash with Dagenham.
Williams joined the Cottagers last January from Portsmouth after graduating from the academy at Fratton Park.
"I've seen him a few times, Andy [Hessenthaler] went to watch him Monday and he goes straight in to our squad for Saturday," Allen told the club's official website.
"He's positive, he can open up defences, he's fast, he's direct and is a good player.
"I know enough people around Fulham who can give me a character reference and a personality reference. I know enough people at Portsmouth so I got enough information over the phone yesterday (Wednesday) what he's actually like off the field, I haven't gone in blind and just taken him.
"He's quick and I thought it would be an area, when playing at home, would help us.
"What I want from him is to take full backs on and get crosses in, playing in to that Rainham End will be fantastic and if he does what I know I have seen him do our supporters will love him.
"If he does well hopefully we may keep him. It's a good deal financially for the club and gives us a position that perhaps we need strengthening."