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The home side were 0-3 at the end of Ryan Sidebottom's opening over, taking him past 700 first-class victims.
The left-armer later bowled last man Tim Murtagh for figures of 5-18, with Tim Bresnan contributing 4-30.
Yorkshire also struggled with the bat in reply, but skipper Andrew Gale made 98 as they reached the close on 238-9.
Their title was confirmed when Notts were bowled out for 204 in their home game with Durham.
Following Middlesex's collapse, they were the only side with a mathematical possibility of denying Yorkshire, but needed the maximum of five batting bonus points to stay in the race, and only managed one.
Yorkshire arrived at Lord's with a 43-point lead over Middlesex, and opted to put them in on a greenish surface after winning the toss.
Sidebottom's third ball trapped Paul Stirling lbw and he had Nick Compton caught behind and bowled Dawid Malan with successive deliveries later in the over.
Debutant Stevie Eskinazi edged to Adam Lyth in the slips and when Bresnan took over from Sidebottom's new-ball partner Jack Brooks, he quickly had Neil Dexter caught behind.
Sam Robson (26) followed in similar fashion and off-spinner James Middlebrook removed John Simpson (28) with the final ball before lunch.
From 92-7 at the interval, Middlesex lost their last three wickets for 14 runs as Sidebottom finished the innings with the final ball of the 33rd over.
Failing to gain any batting bonus points meant the home side could no longer catch Yorkshire in the Division One table, even if they somehow manage to win the match.
The visitors progressed to 129-3 at tea in reply, with Gale - who was not on the field when they won the title in 2014 because of suspension - unbeaten on 54.
The left-hander looked set for a third century of the summer, but was caught at second slip off Neil Dexter (3-24) as he looked to play the ball into the leg-side and the champions slumped from 187-4 to 221-9.
It looked like they might be dismissed before stumps, but bad light brought a slightly premature end with Jack Brooks 12 not out and Sidebottom on nine.
Yorkshire cricket director Martyn Moxon:
"The first win is really special, but given the circumstances this is probably a bigger achievement than winning last year.
"That first over epitomised what Ryan was all about, and to get his 700th wicket as well, he's been a fantastic bowler over the years and there's still a lot of life left in him.
"To combine developing England players with domestic success is a fantastic effort from everyone involved.
"To have provided so many England players this summer and still won the Championship, with two and a half games left, I think it's a remarkable achievement."

Canon Jeremy Pemberton was refused a licence to work as a hospital chaplain by the then acting bishop of Southwell and Nottingham.
Mr Pemberton brought a discrimination case which started in June.
The Nottingham Employment Tribunal heard final submissions from both parties earlier on Tuesday.
Although Mr Pemberton was employed by the NHS, a required licence from the diocese to work at King's Mill Hospital in Mansfield was refused by the Rt Revd Richard Inwood.
He argued that the marriage was against the Church of England's teachings.
Thomas Linden QC, representing the church, said: "The state should not be saying to a religious organisation you can or can't choose this person as your priest.
"The tribunal should say it's clear on the evidence what the church thinks of same sex marriage."
He argued Mr Pemberton went against the doctrine of the church when he entered his same-sex marriage in "a blaze of publicity".
Sean Jones, representing Mr Pemberton, suggested the church would not have had an issue with Mr Pemberton if he was in a civil partnership, even though he claimed they were nearly the same.
He added that nothing stopped clergy from entering into civil partnerships and questioned why it should be different now another type of "civil union which the state calls marriage" has been introduced.
A final conclusion is not expected until next year.
Yorkshire clinched a second consecutive Championship title as a superb bowling display dismissed Middlesex for 106 on the first morning at Lord's.
[NEXT_CONCEPT]
A clergyman may have to wait until next year to find out whether a decision to remove his right to officiate after he married another man was discriminatory.