LIMITED POWER OF ATTORNEY

      The undersigned hereby constitutes and appoints Cindy R. Tahl and J. Scott
Wolchko with full power of substitution, the undersigned's true and lawful
attorney-in-fact to:
      (1) execute for and on behalf of the undersigned, in the undersigned's
capacity as an officer and/or director of Fate Therapeutics, Inc. (the
"Company"), from time to time the following U.S. Securities and Exchange
Commission ("SEC") forms: (i) Form ID, including any attached documents, to
effect the assignment of codes to the undersigned to be used in the transmission
of information to the SEC using the EDGAR System; (ii) Form 3, Initial Statement
of Beneficial Ownership of Securities, including any attached documents; (iii)
Form 4, Statement of Changes in Beneficial Ownership of Securities, including
any attached documents; (iv) Form 5, Annual Statement of Beneficial Ownership of
Securities in accordance with Section 16(a) of the Securities Exchange Act of
1934, as amended, and the rules thereunder, including any attached documents;
(v) Schedule l3D and (vi) amendments of each thereof, in accordance with the
Securities Exchange Act of 1934, as amended, and the rules therew1der, including
any attached documents;
      (2) 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 Form 3, 4
or 5, Schedule 130 or any amendment(s) thereto, and timely file such form(s)
with the SEC and any securities exchange, national association or similar
authority; 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 such
attorney-in-fact's discretion.
      The undersigned hereby grants to each such attorney-in-fact, acting
singly, 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, or 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 or Regulation 13D-G of
the Securities Exchange Act of 1934, as amended. The undersigned hereby agrees
to indemnify the attorney in fact and the Company from and against any demand,
damage, loss, cost or expense arising from any false or misleading information
provided by the undersigned to the attorney-in fact.
      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file such forms 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 March 11, 2019.
/s/ Karin Jooss
Karin Jooss