Their 14-6 win over Wigan Warriors in the Grand Final was Brown's last match with Saints after two seasons.
The club allowed the 41-year-old ex-Huddersfield boss to leave a year early to return to his native Australia.
Cunningham, 37, spent his whole playing career at St Helens before joining the coaching staff after his retirement.
The former Wales and Great Britain hooker made his St Helens debut in 1994 and went on to make 495 appearances at the club.
Cunningham scored the final try at Knowsley Road before the club moved to Langtree Park, and his legendary status has earned him his own statue outside the ground.
"When you finalise what's going on and you agree your contract and everything's done, it's sort of not real," Cunningham told BBC Radio Merseyside.
"It's almost like when your wife's pregnant and you don't see the baby, and the next thing is you sit in the press conference and the baby is there.
"I was never going to say no. It's something that I always dreamed of doing. I started coaching and I was always adamant I was going to be head coach one day. It's the proudest moment of my life.
"It's up there with lifting the trophy for the town at Wembley, I'm so proud to do it."
After his retirement in 2010, following a Grand Final defeat by Wigan, Cunningham joined the Saints backroom staff in an assistant coaching role.
"Keiron is ready for this professionally and totally committed to the task ahead of him," Saints chairman Eamonn McManus told the club website.
"He has been heavily involved in the success of this season and is ideally placed to carry it on for years to come.
"Not only does he understand our culture, he has been instrumental in its development since the inception of Super League."
Super League champions St Helens have named club legend Keiron Cunningham as their new head coach after the departure of Nathan Brown.