Abstract Context. Reconstructing the structure and history of young clusters is pivotal to understanding the mechanisms and timescales of early stellar evolution and planet formation. Recent studies suggest that star clusters often exhibit a hierarchical structure, possibly resulting from several star formation episodes occurring sequentially rather than a monolithic cloud collapse. Aims. We aim to explore the structure of the open cluster and star-forming region NGC 2264 (∼3 Myr), which is one of the youngest, richest and most accessible star clusters in the local spiral arm of our Galaxy; we link the spatial distribution of cluster members to other stellar properties such as age and evolutionary stage to probe the star formation history within the region. Methods. We combined spectroscopic data obtained as part of the Gaia-ESO Survey (GES) with multi-wavelength photometric data from the Coordinated Synoptic Investigation of NGC 2264 (CSI 2264) campaign. We examined a sample of 655 cluster members, with masses between 0.2 and 1.8 M and including both disk-bearing and disk-free young stars. We used T estimates from GES and g,r,i photometry from CSI 2264 to derive individual extinction and stellar parameters. Results. We find a significant age spread of 4-5 Myr among cluster members. Disk-bearing objects are statistically associated with younger isochronal ages than disk-free sources. The cluster has a hierarchical structure, with two main blocks along its latitudinal extension. The northern half develops around the O-type binary star S Mon; the southern half, close to the tip of the Cone Nebula, contains the most embedded regions of NGC 2264, populated mainly by objects with disks and ongoing accretion. The median ages of objects at different locations within the cluster, and the spatial distribution of disked and non-disked sources, suggest that star formation began in the north of the cluster, over 5 Myr ago, and was ignited in its southern region a few Myr later. Star formation is likely still ongoing in the most embedded regions of the cluster, while the outer regions host a widespread population of more evolved objects; these may be the result of an earlier star formation episode followed by outward migration on timescales of a few Myr. We find a detectable lag between the typical age of disk-bearing objects and that of accreting objects in the inner regions of NGC 2264: the first tend to be older than the second, but younger than disk-free sources at similar locations within the cluster. This supports earlier findings that the characteristic timescales of disk accretion are shorter than those of disk dispersal, and smaller than the average age of NGC 2264 (i.e., ≲ 3 Myr). At the same time, we note that disks in the north of the cluster tend to be shorter-lived (∼2.5 Myr) than elsewhere; this may reflect the impact of massive stars within the region (notably S Mon), that trigger rapid disk dispersal. Conclusions. Our results, consistent with earlier studies on NGC 2264 and other young clusters, support the idea of a star formation process that takes place sequentially over a prolonged span in a given region. A complete understanding of the dynamics of formation and evolution of star clusters requires accurate astrometric and kinematic characterization of its population; significant advance in this field is foreseen in the upcoming years thanks to the ongoing Gaia mission, coupled with extensive ground-based surveys like GES.© ESO, 2017. ; This work is based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under program ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. These data have been obtained from the Gaia-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work is also based on observations made with the Spitzer Space Telescope, operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA, and on data from MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. The authors acknowledge useful discussions with S. Sciortino. We also thank V. Kalari, A. Klutsch, and L. A. Hillen-brand for their comments on an earlier version of this manuscript. This work was partly supported by the European Union FP7 program through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR) in the form of the grant >Premiale VLT 2012>. The results presented here benefit from discussions held during the Gaia-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network program. The authors acknowledge support through the PRIN INAF 2014 funding scheme of the National Institute for Astrophysics (INAF) of the Italian Ministry of Education, University and Research (>The Gaia-ESO Survey>, P.I.: S. Randich). S.H.P.A. acknowledges financial support from CNPq, CAPES and Fapemig. M.T.C. acknowledges financial support from the Spanish Ministerio de Economia y Competitividad, through grant AYA2016-75931-C2-1-P.
