T-cells start in the bone marrow as T-cell precursors, then leave the bone marrow to enter the thymus to undergo maturation. Upon maturation they then leave the thymus to enter circulation (blood) and other tissues (e.g. secondary lymphoid tissues). The above diagram shows the immature Double Negative (CD4-/CD8-) T-cell entering the thymus at the corticomedullary junction to eventually progess in the cortex to become Double Positive (CD4+/CD8+) T-cells that undergo further maturation to eventually enter the medullary portion of the Thymus as CD4+/CD8- or CD4-/CD8+ (Single Positive) T-cells.
In summary: the T-cells start as CD4-/CD8-(Double Negative), then become CD4+/CD8+ (Double Positive), and following a MHC induced positive and negative process, they eventually become mature CD4+/CD8- or CD4-/CD8+ (Single Positive) T-cells which will enter blood and various tissues. Note that as opposed to the B-cells which start their early maturation in the bone marrow, T-cells start their maturation process in the thymus. Mnemonic is "B" for B-cells and Bone marrow and "T" for T-cells and Thymus.