Money raised from listing on London's junior AIM market will be used to support the Glasgow club's recovery after one of the most spectacular downfalls in British football.
Scottish champions a record 54 times, Rangers were demoted three levels to the bottom tier of the Scottish game after their parent company was liquidated earlier this year.
Chief executive Charles Green, who took over after the club collapsed, said Rangers and perennial Glasgow rivals Celtic were too big for Scottish football.
"There are now serious talks going on about a restructuring of Scottish football and the European game," he told Reuters.
"There are lots of alternatives. Rangers, being the size it is, will be involved in those restructuring moves. That is where institutions see the growth story."
Rangers lead the Scottish third division by six points after a 3-0 home win over Annan Athletic on Tuesday in front of a crowd of more than 42,000 - a huge attendance for that level of the game.
Clubs from Europe's smaller domestic competitions have periodically talked about combining to try to keep pace with wealthy teams from England's Premier League, Germany's Bundesliga and Spain's La Liga.
"OLD FIRM" REUNITED
Green said he was delighted with a flotation that valued the club at 45 million pounds. Initial market reaction was positive, with shares adding 4 pence to 74 pence by 8.45 a.m British time.
Celtic, which has dominated Scottish football with Rangers for decades, is also listed on AIM. The two clubs, who have an often bitter rivalry, are known collectively as the "Old Firm".
After a series of listings in the 1990s, investors have grown wary of buying stocks in European football clubs whose fortunes are tied up with results on the field and which often spent heavily chasing success.
Manchester United, English champions a record 19 times, bucked the trend by listing in New York in August, valuing the club at $2.3 billion at the time.
Rangers raised 17 million pounds from large institutional investors and 5 million from fans. Investors were left out of pocket earlier this year when the club went bust.
"A week before Christmas, this is an amazing effort from the fans," said Green.
The club planned to limit its wage bill to a third of turnover, a low level by the spendthrift standards of football, and has vowed not to take on bank debt.
"Being demoted to the fourth tier of Scottish football, there is not a huge financial pressure on us," Green said. "It gives us time to structure this business in a way that is financially stable."
($1 = 0.6155 pound)
(Editing by Dan Lalor)