Farrell took over following the 2019 World Cup and led Ireland to a Six Nations Grand Slam earlier this year plus a 17-game winning run that saw them ranked number one by World Rugby and among the favourites to win the World Cup in France.
However, they were beaten in the quarter-finals by New Zealand in Paris in October.
"Coaching Ireland has been a hugely enjoyable experience and I am proud to extend my association with the IRFU," Farrell said in a statement.
"It is a pleasure to work with such a talented and committed group of players and as we enter a new cycle it will be exciting to see more players come through the system.
"There is a talented group of established internationals who are determined to succeed at international level for Ireland and I am excited to see how the recent Ireland U20 squads will also emerge and challenge for... honours in the near future.
"It all makes for an exciting next chapter and it is one which my family and I are delighted to continue."
Farrell, whose previous contract ran until 2025, is fancied to lead the British & Irish Lions' tour of Australia in 2025.
IRFU Performance Director David Nucifora told reporters: “We’d be ecstatic if Andy was named coach of the Lions so hopefully that accolade is the next one for him and we’d be more than comfortable with how to deal with it.
"As far as the period of time he might be away from us, that’s still something I think can be discussed if this happens.”
Capped eight times by England in rugby union and 34 times for Great Britain in rugby league, Farrell was part of England’s staff from 2011 to 2015 before joining the Ireland coaching team in 2016, working under Joe Schmidt.
Ireland will begin the 2024 Six Nations campaign against France in Marseille on February 2nd.
