Although several studies have evaluated one or more linkage services to improve early enrollment in HIV care in Tanzania, none have evaluated the package of linkage services recommended by the Centers for Disease Control and Prevention (CDC) and the World Health Organization (WHO). We describe the uptake of each component of the CDC/WHO recommended package of linkage services, and early enrollment in HIV care and antiretroviral therapy (ART) initiation among persons with HIV who participated in a peer-delivered, linkage case management (LCM) program implemented in Bukoba, Tanzania, October 2014 -May 2017. Of 4206 participants (88% newly HIV diagnosed), most received recommended services including counseling on the importance of early enrollment in care and ART (100%); escort by foot or car to an HIV care and treatment clinic (CTC) (83%); treatment navigation at a CTC (94%); telephone support and appointment reminders (77% among clients with cellphones); and counseling on HIV-status disclosure and partner/family testing (77%), and on barriers to care (69%). During three periods with different ART-eligibility thresholds [CD4<350 (Oct 2014 -Dec 2015, n = 2233), CD4≤500 (Jan 2016 -Sept 2016, n = 1221), and Test & Start (Oct 2016 -May 2017, n = 752)], 90%, 96%, and 97% of clients enrolled in HIV care, and 47%, 67%, and 86% of clients initiated ART, respectively, within three months of diagnosis. Of 463 LCM clients who participated in the last three months of the rollout of Test & Start, 91% initiated ART. Estimated per-client cost was $44 United States dollars (USD) for delivering LCM services in communities and facilities overall, and $18 USD for a facility-only model with task shifting. Well accepted by persons with HIV, peer-delivered LCM services recommended by CDC and WHO can achieve near universal early ART initiation in the Test & Start era at modest cost and should be considered for implementation in facilities and communities experiencing <90% early enrollment in ART care.