One of the major components for realizing quantum computers is the ability to initialize the computer to a known fiducial state, also known as state preparation. While there are promising state initialization approaches based on passive as well as active reset, they either introduce unacceptable overhead for large quantum systems or are unable to prepare an arbitrary quantum state. We demonstrate a state preparation method via measurement-induced steering on digital quantum computers. Arbitrary quantum states are prepared by applying quantum circuits that exploit the back-action caused by measuring part of an entangled state. By delegating ancilla qubits and systems qubits, the initial states are prepared by repeatedly performing the following steps: (1) executing a designated system-ancilla entangling circuit, (2) measuring the ancilla qubits, and (3) re-initializing ancilla qubits to known states through active reset. While the ancilla qubits are measured and reinitialized to known states, the system qubits are steered from arbitrary initial states to desired final states. We show results of the method by preparing arbitrary qubit states and arbitrary qutrit (three-level) states on contemporary, cloud-accessible, quantum computers. We also demonstrate that the state convergence can be accelerated by utilizing the readouts of the ancilla qubits to guide the protocol in an active manner.