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Toraq Wyngard, 53, was due to stand trial on Monday but changed his pleas to guilty, a spokesman for Chester Crown Court said.
He admitted stalking the Hollyoaks actress as well as charges of arson, possession of a bladed article and damaging property.
He set fire to a skip on the driveway of her Cheshire home on September 19 last year, police said.
The court spokesman said Wyngard was due to be sentenced on October 26.
Welch, 63, who played Natalie Barnes in Coronation Street, is a regular panellist on Loose Women and has also appeared on Waterloo Road and as a contestant on Dancing On Ice.