Left footer Askew (22), who can also operate further forward, was part of the Ammies' National League North title-winning squad of 2018 and has since enjoyed loan spells back in the division with Stockport County and Curzon Ashton.
Right-sided Warren (21), meanwhile, is no stranger to life in Lincolnshire having spent a loan spell with the Pilgrims last season – and then a non-contract stint to cover the delayed play-offs.
United manager Craig Elliott was delighted to get the pair signed up to swell his squad numbers to 17 ahead of the Pilgrims' first pre-season friendly this week.
Elliott said: "Josh was somebody that caught my eye in both games last season when we played Curzon Ashton.
"He had a real hunger to sign for us and within the first training session, you could see he was a positive influence on others around him.
"He's at a great age to continue to improve and has already experienced promotion from this league with Salford City.
"I am really pleased to sign Tyrell. I was so impressed with his attitude when he signed for us last season. He was unfortunate not to contribute more in the play-off games but his training standards in that period were excellent.
"I have really high hopes that Tyrell will continue to improve and be a very important player for us."