Terrestrial measurements of neutrinos produced by the Sun have been of great interest for over half a century because of their ability to test the accuracy of solar models. The first solar neutrinos detected with KamLAND provided a measurement of the ^8B solar neutrino interaction rate above an analysis threshold of 5.5 MeV. This work describes efforts to extend KamLAND's detection sensitivity to solar neutrinos below 1 MeV, more specifically, those produced with an energy of 0.862 MeV from the ^7Be electron-capture decay. Many of the difficulties in measuring solar neutrinos below 1 MeV arise from backgrounds caused abundantly by both naturally occuring, and man-made, radioactive nuclides. The primary nuclides of concern were ^210Bi, ^85Kr, and ^39Ar. Since May of 2007, the KamLAND experiment has undergone two separate purification campaigns. During both campaigns a total of 5.4 ktons (about 6440 m^3) of scintillator was circulated through a purification system, which utilized fractional distillation and nitrogen purging. After the purification campaign, reduction factors of 1.5 x 10^3 for ^210Bi and 6.5 x 10^4 for ^85Kr were observed. The reduction of the backgrounds provided a unique opportunity to observe the ^7Be solar neutrino rate in KamLAND. An observation required detailed knowledge of the detector response at low energies, and to accomplish this, a full detector Monte Carlo simulation, called KLG4sim, was utilized. The optical model of the simulation was tuned to match the detector response observed in data after purification, and the software was optimized for the simulation of internal backgrounds used in the ^7Be solar neutrino analysis. The results of this tuning and estimates from simulations of the internal backgrounds and external backgrounds caused by radioactivity on the detector components are presented. The first KamLAND analysis based on Monte Carlo simulations in the energy region below 2 MeV is shown here. The comparison of the Δχ^2 between the null hypothesis and the existence of the ^7Be solar neutrino signal in the data shows a change of 27.9 units, providing evidence that the signal is statistically favored. This analysis reports a measured interaction rate from ^7Be solar neutrinos of R = 343.3 ± 65.0(stat) ± 99.2(syst) events/(kton·day), which corresponds to a total flux of ɸ = (3.41 ±; 1.18) x 10^9 cm^-2 s^-1. The ^7Be solar neutrino flux reported in this work is only the second measurement made of this quantity worldwide. It provides an important cross-check of the Borexino experiment. The flux measurement reported here agrees within 1σ with the standard solar model predictions thus validating our basic understanding of solar fusion reaction processes.