The former Sunderland striker had less than six months left on his contract.
Josh Maja has insisted he and Sunderland "just could not agree" on a new contract.
Maja was in the final six months in his deal when Bordeaux came calling in January, offering top-division football.
And despite claiming to have had offers from England, Germany and Italy, it was in France that the striker chose to continue his career.
Asked what happened during his negotiations with Sunderland, Maja told France Football: "We just could not agree. It's that simple.
"Bordeaux arrived and I wanted to play at a higher level. So I decided to leave."
And according to the 20-year-old, the Ligue 1 side had been following his progress for some time.
"(He was told about Bordeaux's interest) by my agent," explained Maja. "He told me that they had shown interest since last year, so it went back further.
"I made a lot of progress at the beginning of the season, and I think that's when they decided to take action."
Maja agreed his decision to move abroad was "brave", but added: "I felt it was the best opportunity for me to have time in the first team and to progress.
"It was really a higher step up to me compared to League One."
According to Transfermarkt, Sunderland received just £1.5 million for Maja, who scored or made 17 goals in 25 League One games ahead of his transfer.
The Londoner has only appeared five times for his new employers to date, totalling 140 minutes of football.
13th-placed Bordeaux are winless in five and recently hired Paulo Sousa, the former Swansea, Leicester and QPr manager, as boss.
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