Solomon was on Essendon's board in 2025, became an assistant coach this year then took the reins on an interim basis when Brad Scott was sacked.
But battling Essendon won just one game of 12 and Solomon chose not to pursue the full-time role, eventually won by McVeigh ahead of James Hird, Jaymie Graham and Murray Davis.
McVeigh wanted Solomon on his staff but he will return to northern NSW, where his family lives.
"I have been incredibly grateful for the opportunity to give back to a football club that has given me so much," Solomon said in a statement.
"Being asked to coach a club I have a deep-seated connection with, even for a short time, is something I will always be proud of and something I have loved.
"But my family is settled in Northern NSW, and the past few months have shown me that it is just not the right time to be away from my young family year on year.Â
"Their support of me and the club has been incredible, but it is time to go home."
Solomon was adamant Essendon's young list is "made of the right stuff" and urged fans to get behind McVeigh and the players.
The former defender played 158 games for Essendon, including winning the 2000 premiership.
"'Solly' is an Essendon person first and foremost, and that has been obvious in every decision he has made since stepping into the senior coaching role," Essendon president Andrew Welsh, a close friend of Solomon, said.
"Every one of those calls has been made with an eye on where this club is heading rather than on the week in front of him. That is not the easy way to coach, and it takes a particular sort of person to do it.
"He has put connection and passion back at the centre of this place, on and off the field. The work he has put in with our players, our coaches and our staff has been tireless, and this club will feel the benefit of it for years.
"Dean has never once made any of it about himself. That is exactly why he is so well regarded here.
"He did all of it living away from his wife and children. They carried that with him, and our gratitude and thanks go to them as much as to Dean.
"While we'd prefer to have him with us next season, we understand and respect his decision completely."
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