POWER OF ATTORNEY

        KNOW ALL BY THESE PRESENTS, THAT the undersigned hereby constitutes and
appoints each of ALBERTO J. PARACCHINI and LINDSAY CORBY, signing singly, the
undersigned's true and lawful attorney-in-fact to:

        (1)  prepare, execute in the undersigned's name and on the undersigned's
             behalf, and submit to the United States Securities and Exchange
             Commission (the "SEC") a Form ID, Uniform Application for Access
             Codes to File on EDGAR, if necessary, and any other documents
             necessary or appropriate to obtain codes or passwords, as
             applicable, enabling the undersigned to make electronic filings
             with the SEC of reports required by Section 16(a) of the Securities
             Exchange Act of 1934, as amended (the "Exchange Act") or any rule
             or regulation of the SEC;

        (2)  execute for and on behalf of the undersigned, in the undersigned's
             capacity as an officer and/or director of Byline Bancorp, Inc. (the
             "Company"), Forms 3, 4 and 5 (including amendments thereto) in
             accordance with Section 16(a) of the Exchange Act and the rules and
             regulations thereunder, and any other forms or reports the
             undersigned may be required to file in connection with the
             undersigned's ownership, acquisition, or disposition of securities
             of the Company;

        (3)  do and perform any and all acts for and on behalf of the
             undersigned which may be necessary or desirable to complete and
             execute any such Forms 3, 4, 5 or Form ID or other form or report,
             and timely file such form or report with the SEC and any stock
             exchange or similar authority; and

        (4)  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 such
             attorney-in-fact's discretion.

        The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact's 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 attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Exchange Act.

        The undersigned agrees that each such attorney-in-fact herein may rely
entirely on information furnished orally or in writing by the undersigned to
such attorney-in-fact.  The undersigned also agrees to indemnify and hold
harmless the Company and each such attorney-in-fact against any losses, claims,
damages or liabilities (or actions in these respects) that arise out of or are
based upon any untrue statements or omission of necessary facts in the
information provided by the undersigned to such attorney-in-fact for purposes of
executing, acknowledging, delivering or filing Forms 3, 4 or 5 (including
amendments thereto) or Form ID (if any) and agrees to reimburse the Company and
such attorney-in-fact for any legal or other expenses reasonably incurred in
connection with investigating or defending against any such loss, claim, damage,
liability or action.

        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 attorneys-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 12th day of June, 2017.

                                             /s/ Thomas J. Bell III
                                        ------------------------------------
                                                    Signature


                                             Thomas J. Bell III
                                        ------------------------------------
                                                    Print Name