Tremarco, who is 28, joined Caley Jags last summer after making 52 appearances for Tranmere Rovers, 27 for Wrexham and then 89 for Macclesfield Town before spending last season at Maltese Premier League side Floriana, where he played 22 games.
Williams, who will be 26 later this month, played with Kendal Town before joining Chester in October 2012 and moving to Inverness last summer.
Manager John Hughes said: "I've been impressed by the skill and attitude shown by both lads and feel there is more to come yet from Danny and Carl as they continue to adjust to this level.
"I'm pleased they have committed themselves to being part of this club's future."
Hughes, though, has released Norwegian forward Toby Agdestein after his sixth-month deal expired.
The 21-year-old made 15 appearances in all, 14 of which came from the bench.
Hughes added: "Toby has been a bit unfortunate in the amount of game time he got during his spell with the club but we wish him well for the future wherever that may take him.
"We are working hard to get a couple of additions to the squad during the window and we will see where that takes us, but our main priority remains to secure our current squad members."