Welker on Wednesday agreed to a two-year contract worth $12 million guaranteed with the Denver Broncos, one of the Patriots’ chief rivals in the AFC.

The Patriots moved quickly to counter the move, signing former Rams receiver Danny Amendola to a five-year contract worth $31 million, of which $10 million is guaranteed, according to a league source.

Amendola, 27, is 4½ years younger than Welker, 2 inches taller, and more athletic after the catch, similar to Julian Edelman (also a free agent). But Amendola, who had a career-best 85 catches in 2010, has missed 20 games the past two seasons because of injury. Welker missed a total of three in his past eight seasons.

Why did it come to a divorce between Welker, who was beloved by fans and teammates, and the Patriots?

In the end, it was about respect. Welker never thought the Patriots showed enough. Bill Belichick, Robert Kraft, and everyone else associated with the team always spoke of Welker in the highest regard — and they meant those words. But when it comes to athletes, a team shows its true level of respect in dollars — and the Patriots never quite did that with Welker.

It looked as though it was finally going to happen this offseason. Despite trying to prove they could live without Welker early last season, the Patriots gained a new-found respect for his performance as he was the rock in a high-powered passing offense that lost tight ends Rob Gronkowski and Aaron Hernandez, and Edelman for long stretches of the season.

Welker led the NFL in catches (672) and yards (7,459) since 2007, his first season with the Patriots. He is the only receiver in league history to post five 100-catch seasons, and he and Andre Johnson of the Texans are the only ones to have 18 games with 10 or more receptions. Welker stands as the Patriots’ career leader in receptions.

There were good vibes all around at the end of the 2012 season. Welker felt wanted again, and the Patriots talked as if they would have a future together. Both sides felt it was a matter of when and not if Welker would re-sign with the Patriots, especially after Brady redid his contract and freed up $15 million against the salary cap for the next two seasons.

One of the few possible hangups, however, was whether the Patriots would expect Welker to take a discount after playing for the $9.515 million franchise tag in 2012.

And that’s exactly what happened.

The Patriots’ first offer this offseason came in much lower than Welker imagined at two years and $10 million plus incentives. That told Welker two things: His value in the Patriots’ eyes hadn’t changed, and it was time to look for another team.

The Patriots probably thought their offer, if combined with the tag — which they didn’t figure he would play for because he would agree to an extension — was more than acceptable at three years and $19.5 million guaranteed.

The Patriots could have had Welker for the same deal through 2014 — if not a little less — last offseason. But they didn’t do the deal last July, and they expected Welker to give them that discount in any event. But in Welker’s mind, he had to risk his career playing on that one-year tag. Why should he give the team a discount on that now?

In the end, the Patriots expected Welker to pay for their mistake of last offseason, with the help of a down market for free agent receivers. He declined to do that.

But Welker needed to find another team. As of Wednesday morning, there was no market for him; the Patriots appeared to have gauged the market perfectly. The Broncos previously expressed no interest in Welker. Members of their front office didn’t think Welker would be a good fit; they wanted to get better at the tight end position instead.

Perhaps that was a smokescreen, because Broncos sources said many in the front office thought Welker would be a perfect fit — and signing him could weaken a fellow AFC contender at the same time. Team president John Elway might have played possum so the Patriots would think there were no competitors for Welker.

Whether it was a planned deception or not, the Broncos were in perfect position to land Welker if he felt scorned by the Patriots. He did, and both sides quickly pushed toward a deal.