How did americans come to settle in texas when it was part to mexico

Anglo-American colonization in Mexican Texas took place between 1821 and 1835. 

The Spanish government ultimately acquiesced to Austin's request, primarily in an attempt to encourage legal settlement and promote the expansion of Mexican influence in the region. Mexico, at the time, had less than 4,000 residents living in Texas. Spain saw opportunity, along with Austin, in promoting development of the area. Although Moses Austin died in 1823, his son Stephen proved just as determined to encourage rightful settlement of Texas. Stephen Austin, along with the Mexican government, worked to create enticing incentives to drive pioneers to the lands of Texas. Mexico ultimately promised settlers with affordable land grants, provided settlers met several qualifications. Settlers had to become Mexican citizens, speak Spanish and convert to Catholicism to receive land grants. Despite the stringent requirements, settlers flocked to the region. By 1830, more than 15,000 settlers lived in Texas with the encouragement of Mexico.