The former Wimbledon champion will coach the Kazakhstani world number five after he split from the Serbian 24-time Grand Slam champion, 37, in March after helping him win 12 major titles in six years.
Speaking of their partnership, the 25-year-old said: "I’m really looking forward to starting.
"It’s something new for me. I’ve been with one coach for a long time. I want to learn. I’m really happy, and we will see what we can do together."
Rybakina is also a former Wimbledon winner after triumphing at the All England Club two years ago.
Ivanišević and Djokovic started working together in 2018 and he became his main coach in 2022.
But after a disappointing start to the 2024 season, Novak called it quits with his longtime coach, but said their friendship was "always rock solid".
The former world number one posted on Instagram: "I remember clearly the moment I invited Goran to be part of my team. It was back in 2018, and Marian and I were looking to innovate and bring some serve magic to our duo.
"In fact, not only we brought serve, but also lots of laughter, fun, yearend number one rankings, record breaking achievements and 12 more Grand Slams – and a few finals – to the count since then.
"Did I mention a bit of drama too?
"Goran and I decided to stop working together a few days ago. Our on court chemistry had its ups and downs, but our friendship was always rock solid.
"In fact, I am proud to say – not sure if he is – that apart from winning tournaments together, we also had a side bottle in Parchisi going on … for many years.
"And that tournament never stops for us."