Catalyzes the ligation of coenzyme A (CoA) to 4-hydroxybutyrate (4HB). It can also use butyrate, valerate, propionate, acetate and 3-hydroxybutyrate (3HB) as substrates. 4-hydroxybutanoate + ATP + CoA = 4-hydroxybutanoyl-CoA + AMP + diphosphate acetate + ATP + CoA = acetyl-CoA + AMP + diphosphate ATP + CoA + propanoate = AMP + diphosphate + propanoyl-CoA a medium chain fatty acid + ATP + CoA = a medium-chain fatty acyl-CoA + AMP + diphosphate kcat is 0.24 sec(-1) for ligase activity with 4HB as substrate. kcat is 0.23 sec(-1) for ligase activity with butyrate as substrate. kcat is 0.22 sec(-1) for ligase activity with valerate as substrate. kcat is 0.21 sec(-1) for ligase activity with propionate as substrate. kcat is 0.14 sec(-1) for ligase activity with acetate as substrate. kcat is 0.08 sec(-1) for ligase activity with 3HB as substrate. Belongs to the ATP-dependent AMP-binding enzyme family.