Veterans Health Care Improvement Act of 1999 - Amends title XVIII (Medicare) of the Social Security Act to authorize the Secretaries of Health and Human Services (HHS) and Veterans Affairs (VA) (the administering Secretaries) to establish a demonstration project under which the HHS Secretary reimburses the VA Secretary for Medicare health care services furnished to certain veterans at a VA medical facility. Makes eligible for such services a veteran who has attained age 65, is entitled to Medicare benefits, and was enrolled for Medicare benefits on the date of enactment of the Veterans' Equal Access to Medicare Act. Requires voluntary participation of eligible veterans under the demonstration program. Directs the administering Secretaries to establish a data matching program under which there is an exchange of information between HHS and VA to identify those entitled to such benefits. Allows the administering Secretaries to select up to ten demonstration sites in geographically dispersed areas for program participation. Requires at least one site to: (1) be near a base which was closed under a defense base closure law; and (2) serve a predominately rural population area. Requires the demonstration project to be conducted during the three-year period beginning on January 1, 2000. Authorizes the HHS Secretary to waive certain Medicare requirements in connection with the program. Requires the administering Secretaries to submit to the appropriate congressional committees a copy of the demonstration program agreement.

Authorizes the VA Secretary to establish and operate up to four managed health care plans at demonstration sites. Requires such Secretary to submit to the Congress a plan for the use of appropriate sites and entities. Requires certain certifications from the VA Inspector General before a plan may be implemented.

Directs the HHS Secretary to reimburse the VA Secretary for demonstration project services at specified rates. Provides for such payments from Medicare trust funds, with an annual limit of $50 million. Authorizes the reduction of such reimbursement payments for VA failure to maintain its effort level for targeted veterans.

Directs the administering Secretaries to closely monitor the expenditures made under the Medicare program for targeted veterans during the period of the demonstration project compared to expenditures that would have been made for such veterans if the demonstration project had not been conducted. Requires: (1) an annual report by the Comptroller General during each year of the demonstration project; (2) the administering Secretaries to take certain steps in the case of increased costs under the demonstration project; (3) the administering Secretaries to arrange for an independent evaluation of the demonstration project; (4) annual reports from such independent entity during the demonstration project period; and (5) a report from the administering Secretaries on the possibility of extending the demonstration project, making it permanent, or expanding it to cover additional demonstration sites.

(Sec. 3) Amends the Civilian Health and Medical Program of the Uniformed Services (CHAMPUS) to direct the Secretary of Defense to ensure that the health care coverage available through the TRICARE Program (a Department of Defense managed health care program) is substantially similar to the health care coverage available under similar health benefits plans offered under the Federal Employees Health Benefits program. Outlines provisions concerning patient management, reimbursement of health care providers, and the authority for military health care facilities to collect from third-party insurers the costs of health care services provided to covered beneficiaries. Directs such Secretary to report to Congress assessing the effects of the implementation of this section.

(Sec. 4) Expresses the sense of Congress urging the Secretary of Veterans Affairs to: (1) review the policies and procedures of the Veterans Benefits Administration of the VA to identify areas in which such Administration does not currently process claims for veterans' benefits in a manner consistent with objectives set forth in the National Performance Review; (2) initiate necessary actions to process such claims in such manner; and (3) report to Congress on measures taken to improve processing time for such claims.