TRACON Controller reported they vectored an air carrier to a localizer approach at an altitude below MVA. Controller issues a low altitude alert and climbed the aircraft to the appropriate altitude.

Narrative

I was working the combined Radar East ZZZ sector consisting of arrival; departure; and final positions. Weather was moderate VFR when I took the position and pilots were able to accept Visual Approaches to our arrival runways. Soon after I took the position bases to the south began to drop and the aircraft I had on approach could not pick up the airport visually. I obtained a tower visibility report and decided to begin instrument approaches to Runway XX and continue with Visual approaches to Runway XYR for aircraft from the east as the MVA's are much lower. As I began vectoring aircraft to the localizer and GPS approaches to Runway XX I had Aircraft X an E175 check in prior to that determination. I advised them that they could expect a visual approach to Runway XX on initial contact. After the determination to begin instrument approaches I notified all aircraft except for Aircraft X that they could now expect Localizer or GPS approaches to Runway XX. Nonetheless; I vectored Aircraft X to the Localizer and sequenced them into the arrival plan. Once Aircraft X approached the Localizer; the pilot asked if I could give them the RNAV RNP approach to Runway XX. That approach originates approximately 10-12 miles North of their current position. I assumed they meant the GPS X and cleared them for the GPS X (after initially stating GPS Y; and correcting myself) The pilot again asked for the RNAV GPS Y to which I responded that I could not give them that approach from their current position and that I intended to give them a Localizer approach to Runway XX. They accepted and I vectored Aircraft X to join the localizer on a 060 heading and an altitude of 072 which is below the published altitude of the approach(7500) but meets the MVA for the area. Once Aircraft X established on the localizer; I gave them distance from the IAF and cleared them on the LOC approach. I began scanning my traffic and after my scan returned to Aircraft X I observed the aircraft at 067; approximately 500 feet below the MVA. I immediately issued a Low Altitude warning and instructed the aircraft to climb to 075. The aircraft followed instructions and was still in a position to continue with the approach. I asked Aircraft X if they wanted to continue the approach or be re-vectored. The pilot accepted and completed the LOC approach and landed safely. I listened to the audio following the event and realized that I did not advise Aircraft X of my intention to vector them to a LOC approach until they requested the RNAV RNP Y at a distance closely reaching the Localizer approach course. In hindsight; I believe that had I advised the pilots of my intentions in a more timely manner they would have executed a safe and normal LOC approach.