Oh there were plenty of radio signals in space before this, but none that were man made emanating from space. On October 4, 1957, the Soviet Union launched Sputnik 1, into orbit. It was the first man-made satellite. The sphere was about twice the diameter of a basketball and weighed only 183 lbs. Sputnik is the English translation of "Спутник" It just means satellite. it didnt' have much inside other than a thermometer and a battery.
Sergei P. Korolëv was the man in charge of Sputnik. He was very proud of his shining sphere once saying "“This ball will be exhibited in museums!” He was right. A model of it was hing at the Worlds fair. Of course a certain grumpy U.S. intelligent agency made them take it down.
Sputnik had two transmitters. One relayed scientific data on 40.002 Mhz. The other emitted a beep to prove that it existed. Ham radio operators across the world could hear it's beacon beeping out radio signals at 20.005 Mhz. Radio Moscow announced the frequency to encourage shortwave users to tune in. The beeps got louder and then faded with the Doppler Shift. It is often theorized that the 20.005 Mhz frequency was selected because at that point in the solar cycle, that frequency range experienced significant skip. That would ensure that more hams would easily hear the signal. The batteries lasted about 23 days at which point the beep faded and then ceased. I've made a short mix of different recordings.
President Dwight Eisenhower had already been pushing for us to get an American satillite into space. He was not very interested in the scientific data. What he wanted was the legal precedent that space was not owned by we earthlings. Previous to this property ownership was assumed to extend vertically, there was no precedent as to how far. America had also been a proponent of "continental shelf ownership" a sketchy territorial concept that squeezed shipping lanes and helped the oil industry.Anyway Dwight had already seen the photos of Russian launch facilities our U2 flights had produced. He knew it was coming. So he immediately applied pressure on the rocket programs to launch what they had. So the U.S. Army Ballistic Missile Agency duct-taped a bunch of test hardware to a wobbly Vanguard rocket. It exploded on the launch pad. The press mocked it with the nickname "Kaputnik." Only a month later Russia sent up Sputnik 2, which carried the sacrificial dog Laika into orbit. Sputink-1 burned up in orbit about 6 months later.
On Jan. 31, 1958, we did finally sent up a satellite. But it was still just the rmy Ballistic Missile Agency, not NASA that did it. Explorer 1 detected cosmic rays. It was a tad more interesting than Sputniks thermometer. NASA wasnt' formed until July 28th 1958. More here. In 1997 Russian cosmonauts launched a replica of Sputnik 1. This time from from the space station Mir, instead of terra firma. It was smaller than the original Sputnik-1, it recreated the familiar radio beacon. More here.