The Yakovlev design bureau began work on an advanced trainer based on the successful Yak-3 fighter in mid 1944, although the trainer was of low priority owing to the ongoing Second World War. The first prototype of the new trainer, designated Yak-UTI or Yak-3UTI flew in late 1945. It was based on the radial-powered Yak-3U, but with the new Shvetsov ASh-21 seven-cylinder radial replacing the ASh-82 of the Yak-3U. It used the same all-metal wings as the Yak-3U, with a fuselage of mixed metal and wood construction. Pilot and observer sat in tandem under a long canopy with separate sliding hoods. A single synchronised UBS 12.7 mm machine gun and wing racks for two 100 kg (220 lb) bombs comprised the aircraft's armament.
An improved prototype flew in 1946, with revised cockpits and a modified engine installation with the engine mounted on shock absorbing mounts. This aircraft successfully passed state testing in October 1946, with production beginning at factories in Saratov and Leningrad in 1947.
Production Yak-11s were heavier than the prototypes, with later batches fitted with non-retractable tail wheels and revised propellers. A 7.62 mm ShKAS machine gun was sometimes fitted instead of the UBS, while some were fitted with rear-view periscopes above the windscreen. In total, Soviet production amounted to 3,859 aircraft between 1947 and 1955. with a further 707 licence-built by Let in Czechoslovakia as the C-11.
The Yak-11 set five world-class records.
In 1951, Yakovlev revised the design of the Yak-11, adding a retractable tricycle landing gear, with two variants proposed, the Yak-11U basic trainer and Yak-11T proficiency trainer, which carried similar equipment to contemporary jet fighters. The new aircraft had reduced fuel capacity and was unsuitable for operations on rough or snow-covered runways, and so was rejected for Soviet service, although a few examples were built in Czechoslovakia as the C-11U.