Terahertz (THz) wireless data centers can provide low-latency networks and dynamic scalability that are vital for the next-generation cloud computing infrastructure. The knowledge of THz propagation characteristics in a data center environment is essential to the development of novel THz communication systems. However, a comprehensive characterization and modeling of THz propagation channels, which includes various obstructions in a data center is not available. This paper presents results from a THz channel measurement campaign conducted in a data center environment. Various propagation scenarios such as lineof-sight (LoS) link, non-LoS (NLoS) link using existing materials in a data center to redirect the beam, and obstructed-LoS (OLoS),-NLoS (ONLoS) links with common objects in data centers (cables and server racks' mesh doors) serving as obstruction were investigated. Propagation channel parameters such as pathloss and root-mean-squared (RMS) delay spread were analyzed in the aforementioned scenarios while cluster-based modeling was implemented for some scenarios. The proposed model for THz propagation in a data center environment was validated with the measured data. The average inter-arrival time of clusters (1/) and rays (1/λ) are estimated as 4.4 ns and 0.24 ns, respectively. We find that local scattering objects such as server-rack frames/pillars can be used to assist the NLoS type of link, and that cooling airflow in the data center has a negligible impact on THz propagation. Power cables and mesh doors of the server racks can cause additional attenuation of about 20 dB and 6 dB, respectively. Cluster model and other characterization results provided in this work are pertinent to THz wireless system design for data center environments. INDEX TERMS Channel measurements, channel modeling, statistical channel model, terahertz (THz) communications, wireless data centers.