The singer and TV talent show judge - who turns 24 tomorrow - was at London's High Court to accept the "sincere apologies" from rap artist Edwards, who initially denied being responsible for the tape appearing on the web.
Outside court, Miss Contostavlos, read a statement thanking those who had stood by her.
"Today the truth has prevailed. After months of lying to the public and lying in court, Justin has finally admitted to being guilty and I hope justice is served.
She added: "I'm especially grateful for all the support I have received from the public, my friends, family and team. With that support and my determination I have won this battle. Justin messed with the wrong woman."
var tmg_ooyala_embded_tag = "http://player.ooyala.com/player.js?embedCode=tkN2U4NDrh8FbNXz0A_h5c85y-FpWECd&width=460&height=258&deepLinkEmbedCode=tkN2U4NDrh8FbNXz0A_h5c85y-FpWECd&video_pcode=RvbGU6Z74XE_a3bj4QwRGByhq9h2&playerBrandingId=7dfd98005dba40baacc82277f292e522&thruParam_tmgui[relatedVideo]=http%3A%2F%2Fcdn.api.ooyala.com%2Fv2%2Fassets%3Fwhere%3Dembed_code%2Bin%26api_key%3DRvbGU6Z74XE_a3bj4QwRGByhq9h2.WFFAb%26expires%3D1640995199%26signature%3Djy0k5y0KlKnXRvaz8YfB%252Fs1iFHFedXPEda0wTd6P0Fo"+"&thruParam_doubleclick[tagUrl]=" + tmgAdsBuildAdTag("vid", "620x415", "adx", ";dcmt=text/xml;psz=460x315", 3);document.write(''); In an internet statement in March, Tulisa said she was 'devastated' over publication of the tape