•Selective extraction obtains separate extracts of carnosic and rosmarinic acids.•No additional separation steps are needed.•Use of green, eco-friendly, bio-based solvents.•Solvent selectivity is maintained when employed in other extraction techniques.•UAE accelerates the extraction of primary phenolic acids from rosemary. Carnosic (CA) and rosmarinic (RA) acids are the primary phenolic acids in hydrophilic rosemary extracts. Their combination exhibits high antioxidant activity and can be explored in several applications. This study aimed to develop an extraction procedure using bio-based solvents to recover two rosemary extracts, one rich in CA and the other in RA. By using ultrasound-assisted extraction (UAE) and a pool of 34 solvents, we evaluated nominal power (W), extraction time (min), and solvent water percentage (% H2O) regarding yield and selectivity. The authors propose a sequential UAE procedure validated by applying ethanol 99.5 % (v/v), 240 W, and 5 min to recover a rich fraction of 24.0 mgCA.gbiomass−1; followed by a second step using AmAc:LA (1:2 M ratio), 20 % H2O (m/m), 320 W, and 5 min that resulted in 8.4 mgRA.gbiomass−1. Our results indicate that modulating the solvent composition and process temperature is critical to increasing extraction yields and selectivity.