They also refused leave to appeal to the House of Lords, ruling the High Court's original finding of fact over the copyright could not be challenged.
Masquerade Music, based in London, was banned by the High Court in December 1998 from releasing an album of songs from Springsteen's early career.
Ronald Winter, who runs the company, challenged the ruling, saying it allowed inadmissible evidence and applied the wrong standard of proof.
But three judges dismissed the appeal at a hearing on Tuesday morning.
The hearing has centred on detailed evidence of assignments of copyright.
Springsteen's original High Court victory also included an award of £500,000 legal costs against Masquerade, and Lords Justice Waller, Laws and Jonathan Parker also granted him the costs of the appeal.
They also refused leave to appeal to the House of Lords, ruling the High Court's original finding of fact over the copyright could not be challenged.
Damages
Springsteen was told in 1998 he was entitled to damages, to be assessed, for breach of copyright.
Masquerade imported 75 allegedly unauthorised copies of a CD, Before the Fame, in 1997.
The CD featured 19 songs written by Springsteen between 1972 and 1974.
Mr Justice Ferris said then in the High Court that the company "threatened to release many further copies".
The court heard that Springsteen wanted to prevent further copies of recordings being distributed because they had never been legitimately released.
Springsteen had accused the company of pirating the music he first recorded in 1972, before his first album, Greetings From Astbury Park.
Artistic integrity
The singer said Masquerade's attempt to claim ownership of the copyright was an attack on his artistic integrity.
At the time Springsteen said he was simply defending his music.
Mr Justice Ferris banned further distribution of the CDs and told Springsteen he was entitled to damages for breach of copyright against Masquerade and a second company, Flute International Ltd, which was not involved in the appeal.