The baby is said to be healthy and the parents are in great spirits, reported Us magazine.
"The baby is healthy. They have been loving being parents and their friends and family are thrilled," a source said.
Yesterday, Mulligan, 30, made her first red carpet appearance since giving birth at the British Film Institute's London Film Festival. She wore a baggy top and a colorful knee-length skirt.
"The Walker" actress and the "Mumford and Sons" frontman, 28, were previously childhood pen pals before their friendship blossomed into romance in 2011.
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