Exhibit (a)(1)(iii)

OFFER BY

INVESCO SENIOR INCOME TRUST

TO PURCHASE FOR CASH UP

TO 15% OF ITS SHARES FOR 98.5%

OF NET ASSET VALUE

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT

11:59 P.M., NEW YORK CITY TIME, ON DECEMBER 5, 2019

(“EXPIRATION DATE”), UNLESS EXTENDED

THIS OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING

TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN THE

FUND’S OFFER TO PURCHASE AND IN THE LETTER OF TRANSMITTAL.

November 1, 2019

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

We are enclosing herewith the material listed below relating to the offer of Invesco Senior Income Trust, a Delaware statutory trust registered under the Investment Company Act of 1940, as amended, as a diversified, closed-end management investment company (the “Fund”), to purchase up to 15% of its outstanding Common Shares (the “Shares”) upon the terms and subject to the conditions set forth in its Offer to Purchase dated November 1, 2019 and in the related Letter of Transmittal (which together constitute the “Offer”). The price to be paid for the Shares is an amount per Share, net to the seller in cash, equal to 98.5% of the net asset value per Share as determined by the Fund as of the close of ordinary trading on the New York Stock Exchange on December 6, 2019, unless the Expiration Date is extended beyond December 5, 2019.

We are asking you to contact your clients for whom you hold Shares registered in your name (or in the name of your nominee) or who hold Shares registered in their own names. Please bring the Offer to their attention as promptly as possible. No fees or commission will be payable to brokers, dealers or other persons for soliciting tenders for Shares pursuant to the Offer. The Fund will, however, upon request, reimburse you for reasonable and customary mailing and handling expenses incurred by you in forwarding any of the enclosed materials to your clients. The Fund will pay all transfer taxes on its purchase of Shares, subject to Section 4, “Payment for Shares,” of the Offer to Purchase. However, backup withholding at a 24% rate or, in the case of non-U.S. shareholders, 30% withholding under the Foreign Account Tax Compliance Act or 30% withholding at the source may be required unless either an exemption (or lower treaty rate) is proved or the required taxpayer identification information and certifications are provided. See Section 2, “Procedures for Tendering Shares,” of the Offer to Purchase.

For your information and for forwarding to your clients, we are enclosing the following documents:

A letter to shareholders from the Senior Vice President, Chief Legal Officer and Secretary of the Fund and the Offer to Purchase dated November 1, 2019;

The Letter of Transmittal for your use and to be provided to your clients;

Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9;

Notice of Guaranteed Delivery;

Form of letter to clients, which may be sent to your clients for whose accounts you hold Shares registered in your name (or in the name of your nominee); and

Return envelope addressed to the Depositary.

The Offer is not being made to, nor will the Fund accept tenders from, holders of Shares in any State or other jurisdiction in which the Offer would not be in compliance with the securities or Blue Sky laws of such jurisdiction.

As described in the Fund’s Offer to Purchase under Section 2, “Procedures for Tendering Shares,” tenders may be made without the concurrent deposit of Share certificates if (1) such tenders are made by or through an Eligible Guarantor (as defined in the Offer to Purchase); (2) a properly completed and duly executed Notice of Guaranteed Delivery in the form provided by the Fund is delivered to the Depositary prior to 11:59 p.m. New York City time on the Expiration Date; and (3) certificates for tendered Shares (or a Book-Entry Confirmation, as defined in the Offer to Purchase) together with a properly completed and duly executed Letter of Transmittal (or, in the case of book-entry transfer, an Agent’s Message, as defined in the Offer to Purchase), and any other documents required by the Letter of Transmittal, are received by the Depositary within three New York Stock Exchange trading days after execution of a Notice of Guaranteed Delivery.

As described in the Offer, if more than 15% of the Fund’s outstanding Shares are duly tendered prior to the Expiration Date, unless the offer is invalid the Fund will repurchase 15% of the Fund’s outstanding Shares on a pro rata basis upon the terms and subject to the conditions of the Offer.

NEITHER THE FUND NOR ITS BOARD OF TRUSTEES MAKES ANY RECOMMENDATION TO ANY SHAREHOLDER AS TO WHETHER TO TENDER ALL OR ANY SHARES.

Additional copies of the enclosed material may be obtained from the Information Agent at the appropriate address and telephone number set forth in the Fund’s Offer to Purchase. Any questions you have with respect to the Offer should be directed to the Information Agent at its address and telephone numbers set forth in the Offer to Purchase.

Very truly yours,

INVESCO SENIOR INCOME TRUST

Jeffrey H. Kupor

Senior Vice President, Chief Legal Officer and Secretary

Nothing contained herein or in the enclosed documents shall constitute you or any other person the agent of Invesco Senior Income Trust or the Depositary/Information Agent or authorize you or any other person to make any statements or use any material on their behalf with respect to the Offer, other than the material enclosed herewith and the statements specifically set forth in such material.