Despite being the country's leading wicket-takers, Anderson and Broad were left out of the squad with Sir Andrew Strauss making keynote changes in the wake of the 4-0 Ashes defeat in Australia.
Jos Buttler was also left out of the team, but Vaughan believes that the selection made by the interim management team of Strauss and Paul Collingwood will move England forward.
Writing in the Telegraph, Vaughan said: "England want to build a new culture. That's what has led them to the huge decision to drop Jimmy Anderson and Stuart Broad from the squad to the West Indies. They're trying to create a culture away from Broad and Anderson.
"Sometimes high-class senior bowlers can be an issue in the side. That's not saying they're not good people - they are - but you sometimes need to move forward. That sends a strong message to the team."
England will take on West Indies in a three-match Test series which is set to get underway on March 8 in Antigua.
The series represents an opportunity for England to move on from their Ashes capitulation. With that in mind, Vaughan is pleased that the side is moving in a new direction.
He said: "I'm quite happy with this selection. They clearly feel that they need to move away from that pair. That's the message - (captain) Joe Root and his team want to build a new team without Broad and Anderson. The England management have seen something in the pair that has made them want to drop them.
"I think it's smart, what Andrew Strauss has done. This has got the mark of Strauss on it. He's trying to build a new culture. The long-term goal is trying to build a team that can win in Australia.
"In the short term it might be that England are going to take a step back to potentially move forward in the future. But let's remember - England have been losing a lot of Test matches anyway."