The Warwickshire side beat Burton 2-1 in an action-packed final at Welford Road on Saturday to win the prestigious tournament for the first time.
Head coach Norton Bloomfield said: “We are delighted to win. All of the boys played really well.
“Burton were the strongest team we have played in the competition and it made for a thrilling match. The real winner was rugby.”
It was Stratford’s third appearance at the home of Leicester Tigers this season after putting out Ashby in quarter-final and Wymondham 4-3 in the semi-final.
Bloomfield said the success was down to a collective squad effort, and added that his players had also benefited from taking part in Tigers rugby courses.
“They have trained really hard, both as a squad and as an age group, to prepare for this,” he said. “We are really proud of all of them. We had a lot of people from all of the age groups watching and there was a real buzz.
“They have all attended the rugby courses, both at our own club and at local clubs. It all goes to building a rounded player.”
Burton head coach Adam Willetts said his side had done themselves and the club proud in this season's Prima Tiger Cup, which is sponsored by Loughborough-based Prima Solutions.
Willetts said: “I am gutted for the boys, they really put everything into it.
“They did themselves and the club proud. They have been fantastic and have put a lot of hard work into it, and we have had great support from the parents.”
Burton had beaten Holt and three-time former winners Lutterworth at Welford Road in the two previous rounds on their way to the Prima Tiger Cup final.
Willetts said it was a “brilliant achievement” to have reached the final of a nationwide competition which attracted more than 50 entrants.
“I am sure they will roll with the punches,” he said. “They have played three times at Welford Road in as many months. That is a brilliant achievement.”
The Burton side travelled in style for the final after club officials surprised the youngsters by obtaining the England team coach for the trip.
Willetts said: “Mavis and Rita at the club stitched us up – they got the England rugby team coach to take us.
“The first bus came, which was the normal coach, then the England coach came round the corner with the rose on it and everything on it. The children were blown away and so was I. It’s been fantastic for them.”
Tigers will be hosting a Warwickshire rugby course at Kenilworth RFC in the Easter holidays between April 14 and April 17.