KNOW ALL BY THESE PRESENTS, that the undersigned, Arist R. Mastorides,
hereby constitutes and appoints each of Jolyn Sebree and Michael Gernigin and
each of them acting individually, his true and lawful attorneys-in-fact to:

      1. execute for and on behalf of the undersigned Forms 3, 4 and 5 relating
to the Common Stock, par value $0.0001 per share, of Hostess Brands, Inc. (the
"Company") in accordance with Section 16(a) of the Securities Exchange Act of
1934 (the "Exchange Act") and the rules thereunder;

      2. do and perform any and all acts for and on behalf of the undersigned
which may be necessary or desirable to complete the execution of any such Form
3, 4 or 5 and the timely filing of such form with the United States Securities
and Exchange Commission and any other authority, including NASDAQ; and

      3. take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit to,
in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in his or
her discretion.

      The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform all and every act and thing whatsoever requisite,
necessary and proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as such attorney-in-fact
might or could do if personally present, with full power of substitution or
revocation, hereby ratifying and confirming that such attorney-in-fact, or his
or her substitute or substitutes, shall lawfully do or cause to be done by
virtue of this power of attorney and the rights and powers herein granted. The
undersigned acknowledges that the foregoing attorney-in-fact, in serving in such
capacity at the request of the undersigned, are not assuming any of the
undersigned's responsibilities to comply with Section 16 of the Exchange Act.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact. [Signature Page to Power of Attorney]

      IN WITNESS WHEREOF, the undersigned caused this Power of Attorney to be
executed as of this 21st day of January, 2022.

                                          /s/ Arist R. Mastorides
                                          Arist R. Mastorides