Bioadhesive devices can be used to create conformable tissue-device interfaces without suturing. However, the development of such technology faces challenges related to the need for external stimuli or long periods of time for tissue adhesion, fatigue-related breakdown of the stretchable electrodes and the use of solid substrates with non-uniform surface coverage of the tissue. Here, we report a bioelectronic patch that is capable of instantaneous and conformable tissue adhesion on a heart for precise cardiac monitoring. The patch is composed of three layers: an ionically conductive tissue adhesive, a viscoelastic networked film and a fatigue-resistant conducting composite. The system provides conformable tissue adhesion in less than 0.5 s without external stimuli, spontaneous modulus matching based on efficient strain adaptivity and small resistance changes of less than 0.2% at 50.0% tensile strain after 1,000 stretching cycles. We show that the patch can be used for the long-term measurement of electrocardiogram signals (up to four weeks of implantation) in awake rats without causing tissue damage, as well as spatiotemporal mapping in a myocardial ischaemia reperfusion model. A bioelectronic patch that is composed of three layers-an ionically conductive tissue adhesive, a viscoelastic networked film and a fatigue-resistant conducting composite-is capable of instantaneous and conformable tissue adhesion on a heart for precise cardiac monitoring and feedback stimulation.