Captain Sexton helped his country clinch a first championship clean sweep in Dublin - and fourth in total - on the occasion of his final outing in the tournament to reignite the St Patrick's weekend party.
The 37-year-old, who is due to retire following the autumn World Cup in France, kicked nine points to move clear of Ronan O'Gara as the Six Nations' all-time leading scorer with a total of 566.
Head coach Farrell was "immensely proud" of the achievement of his entire squad and singled out influential skipper Sexton for special praise.
"He's been saying all week this is what dreams are made of," said Farrell. "It doesn't come around that often.
"And it's unbelievably fitting that in my opinion the best player ever to play for Ireland is able to sign off on a Grand Slam, on St Patrick's Day, in front of his own crowd.
"There are a lot of stars that have aligned over the course of the last eight weeks and come together this evening."
Ireland's previous Grand Slams - in 1948, 2009 and 2018 - had been clinched in Belfast, Cardiff and London respectively.
Two tries from Dan Sheehan and scores from Robbie Henshaw and Rob Herring took the hosts over the line at a raucous Aviva Stadium.
England led for most of the first half thanks to two Owen Farrell penalties but had Freddie Steward sent off for an arm into the head of Hugo Keenan just before the break and, despite a dogged display, were unable to spoil the party.
"I'm just elated for the boys just to get it over the line because it meant so much to them, especially being here at home, being only the fourth one in Irish history. The first one at home," said Farrell.
"Grand Slams are not just won on nights like this, they're won over the time we've been together. We've been building to this and I'm just glad we've got the job done."
Sexton was afforded a standing ovation as he limped from the field late on following a bruising encounter.
"We've won a Grand Slam, it's pinch yourself stuff," said the fly-half, who claimed his second career Grand Slam but first as skipper.
"It is the stuff of dreams.
"I always wanted to captain Ireland and this fella (Farrell) asked me to do it. That was probably one of the best days of my life and then to have this today, even better."
