Kroenke already owns 40% of the Rams and on Monday saw the expiration of a 60-day deadline in which he had to decide how to proceed with his interest in the club.
Monday's announcement that Kroenke intends to acquire the remaining 60% of the Rams came shortly after his prospects at Premier League club Arsenal took a new twist with reports that Lady Bracewell-Smith, who holds nearly 16% of the club's shares, had appointed bankers to find a buyer.
Kroenke is within a handful of shares of reaching a 30% stake in Arsenal, at which point he would be required to submit a formal takeover bid for the club.
However, his unexpected move for the Rams has come after Illinois businessman Shahid Khan appeared to be in the driving seat for the transaction.
The Rams confirmed in February that Khan had reached an agreement to take a 60% stake in the team after penning an agreement with owners Chip Rosenbloom and Lucia Rodriguez.
"We are pleased to announce that we have exercised our right to purchase the remaining interest in the St Louis Rams football team under the terms of our partnership agreement," Kroenke said in a statement.
"We look forward to working with the Rosenbloom family and the NFL to complete this transaction. We will respect the league and its processes in our efforts to complete this transaction."
A statement released by Rosenbloom added: "Today we received notice that Stan Kroenke has exercised his right of first refusal under the St Louis Rams Partnership Agreement to purchase the Rosenbloom family's controlling interest in the team.
"We and our advisors will work with the National Football League as we move forward with the objective of completing a transaction for the sale of our interest in the Rams."
Kroenke's pursuit of the Rams is set to provide a test of the stringency of the NFL's rules on cross-ownership that prevent owners from having a majority share of an NFL team in one city if they own a majority of another major league team in a different market.
Kroenke currently owns both the Denver Nuggets of the National Basketball Association (NBA) and the Colorado Avalanche of the NHL, along with Major League Soccer's Colorado Rapids.
Speaking at March's NFL owner meetings, commissioner Roger Goodell outlined his stance that the League wasn't prepared to waive its cross-ownership rules for Kroenke, and these regulations are now set to be placed under further scrutiny.
For his part, Khan maintains that he remains dedicated to concluding his takeover of the Rams "if the opportunity presents itself".
"Earlier this evening, Stan advised me that he was going to pursue that opportunity (to purchase controlling interest in the Rams)," he said in a statement.
"I have had the chance to get to know Stan over the past 60 days. As I told Stan during our conversation earlier this evening, I enjoy his company, admire his success in sports, and certainly respect his right to try to purchase the Rosenbloom family's interest in the Rams."
St Louis was without an NFL team from 1988-94, after the League chose Jacksonville when it awarded an expansion team in 1993.
Two years later, late Rams owner Georgia Frontiere, a St Louis native, was persuaded to move the team from Los Angeles back to her hometown and the Rams won the Super Bowl in 1999.
However, the team has endured a tough time on the field of late with a 6-42 record from 2007-09.