A new Senate President is expected to be named sometime after Labor Day.
New Hampshire Republican State Committee Chairman Jennifer Horn praised Bragdon for his decision to step down.
"Senator Bragdon has been an outstanding leader who presided over the New Hampshire State Senate with respect and dignity," she said. "As Senate President, Bragdon has fought to preserve the New Hampshire Advantage and promote fiscally responsible policies that have created economic opportunity for families across the Granite State.
"Senator Bragdon made the right decision, and confirmed that he is a man of high ethical standards and integrity. Republicans are grateful for his exemplary service as the leader of the senate and look forward to his future contributions to the State of New Hampshire."
Gov. Maggie Hassan also issued a statement, calling Bragdon's decision to resign "an appropriate step" given the concerns raised about his new position with the LGC.
"I greatly appreciate his service in that role and have enjoyed working with him to constructively address our challenges," Hassan said. "No matter who is voted by the Senate to be their next president, I look forward to working with him or her to continue moving our state forward through the traditions of hard-work, bipartisanship, and commonsense problem-solving that the people of New Hampshire expect and deserve."