He made the announcement with his onetime rival Mary-Jane Foster at his side as he endorsed her candidacy.
Finch and Foster both lost the Democratic primary to former Mayor Joe Ganim earlier this month.
Foster is running as an independent candidate on the November ballot along with Republican Enrique Torres and Charles Coviello of the New Movement Party as well as Ganim.
Finch failed in his bid to be on the ballot as the candidate for the Job Creation Party after missing a filing deadline.
Ganim's candidacy has drawn fire because he served seven years in federal prison for bribery and corruption related to his time as mayor.
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