The 27-year-old produced a stunning display as Barcelona crushed Sevilla 5-1 at Camp Nou on Saturday, with Messi scoring three.
Former Athletic Bilbao striker Telmo Zarra had held the record for 59 years with 251 goals, but Messi, who scored for the first time in La Liga in May 2005, pulled level 21 minutes into the encounter.
The Argentinian's sublime free-kick found the top-left corner and, although Neymar and former Sevilla captain Ivan Rakitic also found the net, there was no denying that the day belonged to Messi.
The four-time Ballon d'Or winner edged ahead of Zarra with 18 minutes left, sliding in at the back post, and he completed his hat-trick soon after to take his total tally to 253, dedicating the achievement to all those who have helped him in his career so far.
Taking to his official Facebook site, Messi wrote: "When I scored this goal [his first against Albacete], I couldn't imagine I could break any record, let alone this one previously held by the great Telmo Zarra.
"I was only able to achieve this because of the support I have had from so many people during my time here and I would like to dedicate this achievement to you all.
"Thanks for always being with me. I would also like to dedicate this to the people who are no longer with us anymore.
"I will never forget you. Thank you everyone for standing with me!"