(1) Background: It is well-established that coronavirus disease-2019 (COVID-19) is highly pro-inflammatory, leading to activation of the coagulation cascade. COVID-19-induced hypercoagulability is associated with adverse outcomes and mortality. Current guidelines recommend that hospitalized COVID-19 patients should receive pharmacological prophylaxis against venous thromboembolism (VTE). (2) INTERACT is a retrospective, phase IV, observational cohort study aiming to evaluate the overall clinical effectiveness and safety of a higher than conventionally used prophylactic dose of anticoagulation with tinzaparin administered for VTE prevention in non-critically ill COVID-19 patients with moderate disease severity. (3) Results: A total of 705 patients from 13 hospitals in Greece participated in the study (55% men, median age 62 years). Anticoagulation with tinzaparin was initiated immediately after admission. A full therapeutic dose was received by 36.3% of the participants (mean ± SD 166 ± 33 IU/Kgr/day) and the remaining patients (63.9%) received an intermediate dose (mean ± SD 114 ± 22 IU/Kgr/day). The median treatment duration was 13 days (Q1−Q3: 8−20 days). During the study (April 2020 to November 2021), 14 thrombotic events (2.0%) were diagnosed (i.e., three cases of pulmonary embolism (PE) and 11 cases of deep venous thrombosis, DVT). Four bleeding events were recorded (0.6%). In-hospital death occurred in 12 patients (1.7%). Thrombosis was associated with increasing age (median: 74.5 years, Q1−Q3: 62−79, for patients with thrombosis vs. 61.9 years, Q1−Q3: 49−72, p = 0.0149), increased D-dimer levels for all three evaluation time points (at admission: 2490, Q1−Q3: 1580−6480 vs. 700, Q1−Q3: 400−1475, p < 0.0001), one week ± two days after admission (3510, Q1−Q3: 1458−9500 vs. 619, Q1−Q3: 352−1054.5, p < 0.0001), as well as upon discharge (1618.5, Q1−Q3: 1010−2255 vs. 500, Q1−Q3: 294−918, p < 0.0001). Clinical and laboratory improvement was affirmed by decreasing D-dimer and CRP levels, increasing platelet numbers and oxygen saturation measurements, and a drop in the World Health Organization (WHO) progression scale. (4) Conclusions: The findings of our study are in favor of prophylactic anticoagulation with an intermediate to full therapeutic dose of tinzaparin among non-critically ill patients hospitalized with COVID-19.