Broad was kept waiting to join Anderson in the six-strong "500 club" after Monday's fourth-day washout in England's series finale with the West Indies at Old Trafford left him stranded on 499 Test wickets.
The bowler was controversially omitted from England's four-wicket loss in the first Test at Southampton but starred in the series-levelling win at Old Trafford and has been the standout performer in the third Test, also at the Manchester ground.
The 34-year-old has taken eight wickets in the match so far and scored a dashing 62 in England's first innings to change the course of the game.
Strauss, who captained both Broad and Anderson, paid tribute to their longevity.
"They've been a phenomenal opening partnership, that goes without saying," he told reporters. "They are two of England's greatest of all time.
"What has really impressed me with both of them is their hunger to continue. For the two of them to be so hungry is extraordinary."
"I honestly don't believe Stuart Broad has bowled much better than this. There were a couple of years where perhaps he 'lost' his wrist a bit and it was hard work for him bowling to right-handers.
"This series so far he seems to be equally potent against left and right-handers."
Both Broad and Anderson, who turns 38 this week, are at an age where previous new-ball bowlers would have long since retired, although England would, ideally, like them to keep going until the 2021/22 Ashes in Australia.
"For all of us let's write them off at our peril and let's not be in a hurry to pension them off because they have both got a lot more to offer England," said Strauss.
The former skipper also acknowledged the benefit of the competition for places provided by fast bowlers Jofra Archer and Mark Wood, giving England enviable resources to call on.
– 'Something to prove' –
Strauss said the key to Broad's success was his "competitiveness", with the Nottinghamshire seamer revealing he felt "frustrated, angry and gutted" at being left out of the first Test.
Former England captain Andrew Strauss rings the bell before the start of the third Test between England and the West Indies at Old Trafford. POOL/AFP/File/Michael Steele
"He is at his best when he has something to prove," said Strauss. "He's had the bit between his teeth in these last two Test matches and that has served him particularly well over the course of his career."
While England have been able to count on Broad and Anderson, they have struggled for a pair of reliable Test opening batsmen since Strauss's retirement in 2012 ended his partnership with Alastair Cook.
But Strauss has been encouraged by the form of Rory Burns and Dom Sibley, whose partnership of 114 on Sunday was England's first century opening stand in a home Test for four years.
"I think Sibley and Burns at the top of the order are made of the right stuff temperamentally," said former Middlesex left-hander Strauss.
"They've both got quite quirky games, but very effective games. I think that is a big tick."
The ongoing third Test is also supporting the Ruth Strauss Foundation, which the ex-England skipper established after his wife died from a rare form of lung cancer affecting non-smokers in 2018.
This year's #RedForRuth initiative has already raised more than £655,000 ($844,000) compared to last year's inaugural total of over £550,000 during an Ashes Test at Lord's, even though there are no fans at Old Trafford.
Strauss said everyone involved in the Foundation had been "blown away" by the public support, adding: "For us to have gone sailing past what we raised last year is almost beyond belief."