The pair became man and wife in Las Vegas last week.
Peaches, 19, is believed to have met Harvard graduate Maxwell 2 years ago. The multi-instrumentalist is in a 'power pop' duo called Chester French.
Last month Peaches co-presented the ITV I-Tunes festival in London and hooked up again with Max.
The teenager and her new husband, 23, have 'the full support of their family and friends', confirms a press release. They do not want 'unnecessary publicity'.