A representative of Presley, 48, confirmed that she wants full custody of the couple's twin daughters after citing irreconcilable differences as the grounds for the split, reported E! online.
The post-nuptial agreement made by the pair will make the divorce proceedings simpler.
Elvis Presley's daughter got married to Lockwood in 2006 and have twin seven-year-old daughters, Harper Vivienne Ann and Finley Aaron Love.
The singer is running high on success in the music industry with albums and hit singles including "Lights Out" and "Over Me."