A method for installation of a monopile adapted to support an offshore wind turbine, wherein use is made of an installation vessel comprising: - a hull, - a crane mounted on the hull, - a motion compensating integrated pile upending and holding device, the device comprising: - a motion compensating support assembly mounted to the hull of the vessel, - a pile holder that is supported by the support assembly and is tiltable about a tilt axis relative to the support assembly between a horizontal orientation and a vertical orientation, wherein the pile holder is configured to receive a lower end portion of the monopile in a horizontal orientation thereof and to support the lower end portion, wherein the device is configured to allow for upending of the monopile into a vertical orientation thereof by means of the crane of the vessel whilst the lower end portion remains received and supported by the pile holder, wherein the pile holder is configured to guide the monopile in said vertical orientation, at least as the monopile is being lowered by the crane during landing of the monopile on the seabed, wherein the motion compensating support assembly comprises controllable motion actuators (206, 207) and an associated motion control unit configured for position control of the monopile during landing of the monopile on the seabed and/or control of verticality of the monopile during driving of the monopile into the seabed so as to compensate for vessel motion, wherein the method comprises, with the hull of the vessel in floating condition: - receiving the lower end portion of a monopile in the pile holder while being in a horizontal orientation, - upending the monopile by lifting an upper end portion of the monopile by means of the crane while the lower end portion remains received and supported by the pile holder, so that the monopile is upended into vertical orientation thereof, - lowering the upended monopile by means of the crane whilst being guided by the pile holder so that the monopile is landed on the seabed, - driving the monopile deeper into the seabed, e.g. involving the use of pile driving equipment, characterized in that during at least a phase of the upending of the monopile, one or more of the controllable motion actuators (206,207) of the motion compensating support assembly are operated to provide controlled motion of the lower end portion of the monopile so as to reduce swing motion of the monopile. - a hull, - a crane mounted on the hull, - a motion compensating integrated pile upending and holding device, the device comprising: - a motion compensating support assembly mounted to the hull of the vessel, - a pile holder that is supported by the support assembly and is tiltable about a tilt axis relative to the support assembly between a horizontal orientation and a vertical orientation, - a motion compensating support assembly mounted to the hull of the vessel, - a pile holder that is supported by the support assembly and is tiltable about a tilt axis relative to the support assembly between a horizontal orientation and a vertical orientation, wherein the pile holder is configured to receive a lower end portion of the monopile in a horizontal orientation thereof and to support the lower end portion, wherein the device is configured to allow for upending of the monopile into a vertical orientation thereof by means of the crane of the vessel whilst the lower end portion remains received and supported by the pile holder, wherein the pile holder is configured to guide the monopile in said vertical orientation, at least as the monopile is being lowered by the crane during landing of the monopile on the seabed, wherein the motion compensating support assembly comprises controllable motion actuators (206, 207) and an associated motion control unit configured for position control of the monopile during landing of the monopile on the seabed and/or control of verticality of the monopile during driving of the monopile into the seabed so as to compensate for vessel motion, wherein the method comprises, with the hull of the vessel in floating condition: - receiving the lower end portion of a monopile in the pile holder while being in a horizontal orientation, - upending the monopile by lifting an upper end portion of the monopile by means of the crane while the lower end portion remains received and supported by the pile holder, so that the monopile is upended into vertical orientation thereof, - lowering the upended monopile by means of the crane whilst being guided by the pile holder so that the monopile is landed on the seabed, - driving the monopile deeper into the seabed, e.g. involving the use of pile driving equipment, - receiving the lower end portion of a monopile in the pile holder while being in a horizontal orientation, - upending the monopile by lifting an upper end portion of the monopile by means of the crane while the lower end portion remains received and supported by the pile holder, so that the monopile is upended into vertical orientation thereof, - lowering the upended monopile by means of the crane whilst being guided by the pile holder so that the monopile is landed on the seabed, - driving the monopile deeper into the seabed, e.g. involving the use of pile driving equipment, characterized in that during at least a phase of the upending of the monopile, one or more of the controllable motion actuators (206,207) of the motion compensating support assembly are operated to provide controlled motion of the lower end portion of the monopile so as to reduce swing motion of the monopile.