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Diddy 's making good on his promise to appeal his conviction and sentence in his federal criminal case ... TMZ has learned.

According to new legal docs, filed in federal court in New York and obtained by TMZ, the notice was filed Monday and lists Alexandra A.E. Shapiro as his counsel. We're told Diddy's team will likely file their substantive brief for the appeal within 4 to 6 weeks. Play video content

As you know ... the Bad Boy mogul was sentenced back on October 3 by Judge Arun Subramanian to serve a little over 4 years in a federal prison.

He was convicted on 2 charges of transportation across state lines for the purpose of prostitution, AKA the Mann Act.

Diddy was acquitted on the more serious counts of racketeering and sex trafficking. Gallery Launch Gall

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