Stewart, aged 23, has already made 17 appearances for the first team while Alexander-Arnold, 18, made his debut in last month's EFL Cup victory over Tottenham.
Woodburn, 17, featured in a couple of pre-season friendlies and has continued to impress for the under-23s.
"This is really positive news of course, and it's brilliant we have acted decisively to show our intent with our young players," Klopp told the official site.
"With Kev it is maybe a little different. He is of course established with us now and making a contribution as an important member of our first-team squad.
"Trent spends most of his time with the first team in this moment and is progressing each and every day.
"Ben is in those earlier stages and has a lot of developing to do still - but wow, what an exciting talent he is.
"All three of these players are big talents and are at different stages of their development, but it is development that is key and they must continue to learn and improve to achieve their full potential.
"News like today makes it exciting for me and the first-team staff that their development will continue with us at LFC."