Last month, the European Tour won its legal battle with rebels after the players appealed against punishments the tour wanted to impose on those who took part in the inaugural LIV event last year.
Ryder Cup stars Garcia, Poulter and Westwood will not be eligible for the matches against the United States in Rome later this year.
"(The tour) would like to take this opportunity to thank the four players for the contribution they have made to the Tour and in particular to Sergio, Ian and Lee for the significant part they have played in Europe's success in the Ryder Cup over many years," the European Tour said in a statement.
"Their resignations, however, along with the sanctions imposed upon them, are a consequence of their own choices."
Former world number one Westwood, 2017 Masters champion Garcia and Poulter have 53 European Tour victories between them.
Twelve players, including Westwood, Poulter and Bland, appealed against the sanctions imposed last year.
The case arose when players requested releases to play in the LIV Golf event at the Centurion Club in England in June last year.
Those requests were denied but the players competed regardless and were fined £100,000 ($125,000) and suspended from the Scottish Open and two other events.
Garcia was among four players to withdraw from the legal case, which was heard behind closed doors by Sports Resolutions UK in February.
The players could have opted to appeal again.
Europe will be without three of its biggest Ryder Cup stars when the event gets underway in September.
Spain's Garcia holds the record of 28.5 points, while Westwood has competed in 11 Ryder Cups, a European record he shares with Nick Faldo.
Poulter is best known for his Ryder Cup exploits, notably inspiring Europe's remarkable comeback in the 'Miracle at Medinah' in 2012.
The European Tour said it would provide an update on other sanctioned players on Thursday.
Englishman Bland became the oldest first-time winner in European Tour history aged 48 when he won the 2021 British Masters.
