Peter Martin's A Life of James Boswell has been hailed as the definitive biography of the great biographer. This may be a bit of an exaggeration as the two-volume biography by Frederick Pottle and Frank Brady (the volumes of which were published in 1966 and 1984 respectively) is more detailed and much better annotated.
Still, Martin has drawn fully on previous research and has written a biography which is both interesting and entertaining, without all those small details which a casual reader might find tedious.
A Life of James Boswell was published in Hardcover in 1999 and in Paperback in 2000, and it has been reprinted at least once, in 2002.
This book should be available from all major online bookstores, and used copies are readily available from AbeBooks.