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We derive absolute dimensions of the early B-type detached eclipsing binary V453 Cygni (B0.4 IV + B0.7 IV, P= 3.89 d), a member of the open cluster NGC 6871. From the analysis of new, high-resolution spectroscopy and the UBV light curves of Cohen, we find the masses to be 14.36 ± 0.20 and 11.11±0.13 M_☉, the radii to be 8.55±0.06 and 5.49±0.06 R_☉, and the effective temperatures to be 26600±500 and 25500±800 K for the primary and secondary stars, respectively. The surface gravity values of logg= 3.731±0.012 and 4.005±0.015 indicate that V453 Cyg is reaching the end of its main-sequence lifetime. We have determined the apsidal motion period of the system to be 66.4±1.8 yr using the technique of Lacy extended to include spectroscopic data as well as times of minimum light, giving a density concentration coefficient of logk₂=-2.226±0.024. Contaminating (third) light has been detected for the first time in the light curve of V453 Cyg; previous analyses without this effect systematically underestimate the ratio of the radii of the two stars. The absolute dimensions of the system have been compared with the stellar evolution models of the Granada, Geneva, Padova and Cambridge groups. All model sets fit the data on V453 Cyg for solar helium and metal abundances and an age of 10.0±0.2 Myr. The Granada models also agree fully with the observed logk₂once general relativistic effects have been accounted for. The Cambridge models with convective core overshooting fit V453 Cyg better than those without. Given this success of the theoretical predictions, we briefly discuss which eclipsing binaries should be studied in order to challenge the models further.