Neil Warnock has ruled himself out of becoming Sheffield Wednesday's manager, claiming the move would be too divisive.
Manchester United midfielder Shinji Kagawa has admitted it should be no problem for him to play on the left.
The 25-year-old, who scored 12 goals for his Primera Division club last season, has signed a long-term contract with the Reds after passing his medical at Melwood.
Liverpool did not disclose the transfer fee but it is believed to be around £7.7million.
Celta's successful fight against relegation from the Primera Division on the final day of the season earlier this month held up progress.
The Spaniard is Liverpool's third signing of the summer after deals for Manchester City defender Kolo Toure and the capture of Luis Alberto from Sevilla.