Zaidi, 32, has joined on a two-year contract after the Pakistani-born player made his debut for Sussex in the County Championship match with Yorkshire in September after he had joined on a non-contract basis.
The slow left-armer took 4-57 in his first game, while he also showed his capability with the bat in the victory over champions Durham, when he made 45.
Zaidi, who has played for Pakistan A, is a British citizen so is not classed as an overseas player.
He said: “It is an honour to sign for Sussex, and this is a really big achievement for me, especially after a few years’ break from the pro game. I’m really grateful for the chance that they have given me.”
Lewis has joined Sussex on a one-year contract after being released by Surrey at the end of the season.
He made his first-class debut in 1995 and has taken more than 800 wickets in the four-day format, both with Gloucestershire and more latterly Surrey, where he has spent the last two seasons.
He has also taken more than 300 wickets in List A competition and claimed 62 scalps in Twenty20 cricket and has played for England across all three formats of the game.
Lewis said: “I’m really excited to be joining Sussex, a club I have admired from a distance for a long time and I’m looking forward to a new challenge in my career.
“I am really confident that I can make valuable contributions to the team across all competitions. Sussex have a strong squad that, in my opinion, is close to winning more trophies and I want to help them achieve this.”