In this article, we propose a wirelessly powered Internet-of-Things (IoT) system based on the cell-free massive MIMO technology. In such a system, during the downlink phase, the sensors harvest radio-frequency (RF) energy emitted by the distributed access points (APs). During the uplink phase, sensors transmit data to the APs using the harvested energy. Collocated massive MIMO and small-cell IoT can be treated as special cases of cell-free IoT. We derive the tight closed-form lower bound on the amount of harvested energy, and the closed-form expression of SINR as the metrics of power transfer and data transmission, respectively. To improve energy efficiency, we jointly optimize the uplink and downlink power control coefficients to minimize the total transmit energy consumption while meeting the target SINRs. Extended simulation results show that cell-free IoT outperforms collocated massive MIMO and small-cell IoT in terms of both downlink and uplink 95% likely performances. Moreover, significant gains can be achieved by the proposed joint power control in terms of both per user throughput and energy consumption.