In 1921, when the electrification of the Swiss network was quickly progressing, the SBB ordered an electric shunter to replace three-axle tank locomotives, there called E 3/3. Two prototypes were delivered in 1923 which had three driven axles and an additional carrying axle to keep the axle load down. These were called Ee 3/4, but no further locomotives of the same design were ordered. The production variant was introduced in 1928. It only had three axles, which were driven via a crank axle and coupling rods.
The first production batches had an output of 428 kW, a starting tractive effort of 88 kN and top speed was 40 km/h. The first locomotives had their cab on one end, but all others got a central cab for better view in both directions. More batches followed until 1966, for a total of 136. Weight grew from 39 to 45 tonnes, while the output now was 508 kW. Starting tractive effort was first increased to 98 and then to 118 kN. Top speed of the later batches was 50 km/h, so they were sometimes even used for light freight trains. With the increase in freight train speeds over the years, they were only used for shunting. The last locomotives from the newer batches were withdrawn in 2020. Six have been preserved and at least 16383 is still in working condition.
While the basic variant was only equipped for 15 kV AC, there were two developments of the Ee 3/3 which could also run under other systems in the neighboring countries. The first was the Ee 3/3II that could also operate on French lines electrified with 25 kV AC. 15 of this were built from 1957. Additionally, ten four-system locomotives called Ee 3/3IV were built from 1962. These could also run under DC with either 1,500 or 3,000 Volts, for service on the French DC lines and in Italy.