The US internationalist played his last game for Orlando City in the 3-1 defeat by Nashville SC in the MLS Cup play-offs on Wednesday night at the Nissan Stadium and will head to Scotland next week to settle into the club and city ahead of his official arrival on January 1, two days before the derby.
Speaking to the media ahead of Hibs’ trip to Perthshire to face St Johnstone, Ross said: "Chris Mueller will arrive in the UK on Wednesday [December 1], which will give him a month with us before he's ready to play.
"It gives him time to settle at the club and in the city. He has always earmarked the derby as his first game to be involved in."
Writing on social media in the aftermath of the defeat by Nashville Mueller said: “Words can’t express the gratitude I feel in my heart for getting to spend the past four years in our city. I will cherish the experiences I’ve had, people I’ve met, and memories I’ve created for the rest of my life.
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“Thank you Orlando, from the bottom of my heart.”
The 25-year-old signed a pre-contract with the Easter Road side in July and will make the move to the Capital having scored 22 goals and registered 20 assists in 126 games for the Lions.
Fellow new signing Dylan Tait won’t be involved against Hearts as the midfielder is due to play in Raith Rovers' Fife derby with Dunfermline Athletic on January 2.