He will continue to work for Saints as a technical coaching consultant, supporting new director of rugby Phil Dowson and head coach Sam Vesty.
And Saints will hope to continue the fine work that has been done after they finished fourth in the Gallagher Premiership.
Biggar, like Boyd, arrived at Saints in the summer of 2018, and he has since gone on to become Wales captain, starring for club and country.
And the fly-half said has hailed the way Boyd has steered the Saints ship, while bringing the best out of individuals, including himself.
Biggar said: "t's really difficult to keep everyone happy when you're the director of rugby because you've got to drop people, tell people they haven't got contracts whatever it is, but the best way I can describe Boydy is that there won't be too many people who will have a bad word to say about him, as a bloke and a director of rugby.
"That's pretty rare when you've got to tell boys they're not playing or there's no contract.
"It's black and white, there's no grey areas with him.
"He's been a breath of fresh air really.
"When things have been tough, he's brightened it up and taken a lot of pressure on himself.
"When things have been good, he's kept us all grounded and working really hard.
"I'm eternally grateful for what he's done for my career - I feel he's rejuvenated me.
"Between him and Sam Vesty, they are both absolutely world class coaches."
Saints saw their season end on Saturday as they were beaten 27-14 by Leicester Tigers in the Premiership play-off semi-final at Mattioli Woods Welford Road.
It was a case of what might have been for Boyd's side as they squandered some big chances during the first half of a game they dominated for long spells.
"When we had the ball, we moved it quite well," Biggar said.
"We left a couple of golden chances out there.
"The chances we created were quite good chances and we'd back ourselves to finish them quite often.
"All of a sudden we couldn't get the scoreboard pressure to apply on Leicester.
"We'll learn from this and we know that in big games away from home we need to take our chances, otherwise it's going to come back to bite us."
Saturday's game came at the end of an emotional week for Leicester as the wife of Tom Youngs recently passed away.
There was a minute's applause before the game, and Biggar spoke to Tigers scrum-half Ben Youngs, brother of Tom, at full-time.
"I was again offering condolences and saying I hope everything can be as well as it can be, which is a bit of a hollow thing to say," Biggar told Planet Rugby.
"It showed immense character from him (Ben Youngs) to be able to focus on a game of rugby.
"There was a massive amount of pride and character from him.
"I'm really disappointed we lost the game, but I suppose if we were going to lose to anyone this week then it's probably nice for them as a club to get that win."