The newspaper had said it would appeal to the House of Lords after it lost an earlier appeal in January over a report in 2003 saying Galloway had been "in the pay" of Saddam Hussein, the former Iraqi leader.
On Thursday, the paper said it had dropped the case.
The newspaper based its story on documents it said it found in the abandoned Iraqi foreign ministry building in Baghdad after the invasion to topple Saddam in 2003.
The report claimed that Galloway had received £375,000 a year from the Iraqi government, something he had always denied.
A spokeswoman for the newspaper said "the Telegraph Group has decided not to petition for leave to appeal".
The paper had argued that it was in the public interest to publish the documents.
Galloway, 51, was kicked out of the Labour party for his outspoken opposition to the Iraq war and last year became an MP for the Respect party.
His two-week appearance in reality TV show Celebrity Big Brother last month angered many of his constituents in east London who felt that his time would have been better spent representing their interests in parliament.
"I put everything I had on the line in this case and I have been totally vindicated. I'm obviously delighted to have finally won but I'm extremely vexed that this has taken so long to settle"
MP, Respect party
Galloway said the Telegraph would have to pay the legal costs of both sides.
In a statement, Galloway said: "I put everything I had on the line in this case and I have been totally vindicated.
"I'm obviously delighted to have finally won but I'm extremely vexed that this has taken so long to settle."