The Glasgow club decided against utilising a second £5m loan agreed with fellow shareholder Mike Ashley's Sports Direct retail company.
The Newcastle United owner loaned an initial £5m to the club in January.
Rangers say the new loans will be used as working capital and run until 31 December to give them "time to deliver a longer-term funding solution".
Scottish businessmen Park, Letham and Taylor, known collectively as the Three Bears, had a £5m investment plan rejected by the Scottish Championship club in December.
Rangers, who at the time had Ashley's former business colleague, Derek Llambias, as chief executive, instead agreed a deal with the Englishman to keep the club from going out of business in an arrangement that gave them the facility to draw a further £5m.
But South Africa-based businessman Dave King this month won a vote among shareholders at an extraordinary meeting he called to replace the Glasgow club's board.
And his successful group have since appointed Park to the board.
Paul Murray is filling in as interim chairman while King waits to see if his appointment meets with approval from the Scottish football authorities.
"We can and we will rebuild the club and this £1.5m investment is stage one of the process," said Murray, who also revealed King would be "invited to invest" once the Scottish FA complete their review of his status.
Murray was also critical of the previous regime, with a club statement making reference to "years of gross mismanagement".
"Many of the people who have occupied the Ibrox boardroom during that period should be ashamed of themselves for the parts they played in dragging this great institution towards near financial ruin," he said.
"It is actually difficult to look closely at the club's finances and understand the rationale behind some of the decisions taken."
Rangers have agreed loans totalling £1.5m from shareholders Douglas Park, George Letham and George Taylor.