Bowman, 24, has agreed a two-year contract after joining from Gateshead for an undisclosed fee.
Belic, 20, has joined on an initial six-month loan from West Ham United, replacing Marvin Johnson, who moved to Oxford United for an undisclosed fee.
Motherwell manager Mark McGhee told the official website: "Luka is a wiry forward player who can play through the middle or on the flanks."
He continued: "He works extremely hard, particularly without the ball, and knows where the net is. He'll give us competition.
"With the arrival of Ryan, it allows us to set up in a 4-3-3 formation, which has brought great success in the past, particularly last season.
"We've tracked him for some time now, but today's developments have allowed us to go and get him.
"He's been top scorer for his clubs over the last two seasons, he's big, powerful, good in the air and runs in behind."
Bowman scored 16 goals in 41 appearances last season for National League outfit Gateshead - and three goals in seven this season.
He has previously had spells at Torquay United, York City, Hereford, Darlington and Carlisle United.
Bowman said: "It's a different league and a different competition, so it's a challenge, but I'm just excited to get going."
Capped by Serbia up until under-19 level, Belic recently signed a new contract with West Ham.
Meanwhile, Motherwell have released 24-year-old Lee Lucas, the former Cheltenham midfielder having made one appearance after arriving in the summer.
Defender Luke Watt has joined Stranraer on loan until January.
Motherwell have signed striker Ryan Bowman and winger Luka Belic.