Seymour stayed with Pompey for the duration of the 2020-21 season before he was released in the summer before joining Burgess Hill.
The stopper made 26 appearances in all competitions for the Hillians, keeping eight clean sheets in the process.
The 20-year-old was the Reds' trialist goalkeeper in Wednesday’s friendly against a Tottenham Hotspur XI.
Seymour said: "I’m really happy to be here and back into professional football.
"A big thank you to the gaffer and Dean [Lightwood] for allowing me to come in a train over the last few months and then give me this fantastic opportunity to come in full time with the club until the end of the season.”
Seymour later tweeted: "Would just like to say a massive thankyou to everyone involved at @Official_BHTFC for this season getting me back playing and enjoying football.
"Wish you nothing but the best for the season and future. #hillianshilliansboingboing."
Reds boss John Yems said: "I’m happy to welcome young Taylor to the squad, he is a promising young goalkeeper and has been training with us for some time.
"He will be able to learn from the experienced Glenn Morris which will be great for his game. I wish him all the best here at Crawley."
Crawley Town chief executive Erdem Konyar said: "Taylor is a very promising local young goalkeeper who we are delighted to add to our ranks. I wish him all the best."
Burgess Hill Town tweeted: "The club can confirm that Taylor Seymour has signed for @crawleytown.
"We would like to thank Taylor for his time at the club and wish him all the very best for the future. Good luck, @Taylor_Seymour1!"
Hill manager Jay Lovett also tweeted: "Good luck mate and fully deserved. Goes to show when you put in the performances, good things happen.
"I'd like to thank you for everything you done for us and look forward to watching you continue to progress. Top GK!! Great lad!! @Taylor_Seymour1 @Official_BHTFC"
Seymour has travelled to Northampton with the Crawley squad for this (Saturday) afternoon’s Sky Bet League Two meeting.